Quantum Theory

I INTRODUCTION

Quantum Theory, in physics, description of the particles that make up matter and how they interact with each other and with energy. Quantum theory explains in principle how to calculate what will happen in any experiment involving physical or biological systems, and how to understand how our world works. The name “quantum theory” comes from the fact that the theory describes the matter and energy in the universe in terms of single indivisible units called quanta (singular quantum). Quantum theory is different from classical physics. Classical physics is an approximation of the set of rules and equations in quantum theory. Classical physics accurately describes the behavior of matter and energy in the everyday universe. For example, classical physics explains the motion of a car accelerating or of a ball flying through the air. Quantum theory, on the other hand, can accurately describe the behavior of the universe on a much smaller scale, that of atoms and smaller particles. The rules of classical physics do not explain the behavior of matter and energy on this small scale. Quantum theory is more general than classical physics, and in principle, it could be used to predict the behavior of any physical, chemical, or biological system. However, explaining the behavior of the everyday world with quantum theory is too complicated to be practical.

Quantum theory not only specifies new rules for describing the universe but also introduces new ways of thinking about matter and energy. The tiny particles that quantum theory describes do not have defined locations, speeds, and paths like objects described by classical physics. Instead, quantum theory describes positions and other properties of particles in terms of the chances that the property will have a certain value. For example, it allows scientists to calculate how likely it is that a particle will be in a certain position at a certain time.

Quantum description of particles allows scientists to understand how particles combine to form atoms. Quantum description of atoms helps scientists understand the chemical and physical properties of molecules, atoms, and subatomic particles. Quantum theory enabled scientists to understand the conditions of the early universe, how the Sun shines, and how atoms and molecules determine the characteristics of the material that they make up. Without quantum theory, scientists could not have developed nuclear energy or the electric circuits that provide the basis for computers.

Quantum theory describes all of the fundamental forces—except gravitation—that physicists have found in nature. The forces that quantum theory describes are the electrical, the magnetic, the weak, and the strong. Physicists often refer to these forces as interactions, because the forces control the way particles interact with each other. Interactions also affect spontaneous changes in isolated particles.

II WAVES AND PARTICLES

One of the striking differences between quantum theory and classical physics is that quantum theory describes energy and matter both as waves and as particles. The type of energy physicists study most often with quantum theory is light. Classical physics considers light to be only a wave, and it treats matter strictly as particles. Quantum theory acknowledges that both light and matter can behave like waves and like particles.

It is important to understand how scientists describe the properties of waves in order to understand how waves fit into quantum theory. A familiar type of wave occurs when a rope is tied to a solid object and someone moves the free end up and down. Waves travel along the rope. The highest points on the rope are called the crests of the waves. The lowest points are called troughs. One full wave consists of a crest and trough. The distance from crest to crest or from trough to trough—or from any point on one wave to the identical point on the next wave—is called the wavelength. The frequency of the waves is the number of waves per second that pass by a given point along the rope.

If waves traveling down the rope hit the stationary end and bounce back, like water waves bouncing against a wall, two waves on the rope may meet each other, hitting the same place on the rope at the same time. These two waves will interfere, or combine (see Interference). If the two waves exactly line up—that is, if the crests and troughs of the waves line up—the waves interfere constructively. This means that the trough of the combined wave is deeper and the crest is higher than those of the waves before they combined. If the two waves are offset by exactly half of a wavelength, the trough of one wave lines up with the crest of the other. This alignment creates destructive interference—the two waves cancel each other out and a momentary flat spot appears on the rope. See also Wave Motion.

A Light as a Wave and as a Particle

Like classical physics, quantum theory sometimes describes light as a wave, because light behaves like a wave in many situations. Light is not a vibration of a solid substance, such as a rope. Instead, a light wave is made up of a vibration in the intensity of the electric and magnetic fields that surround any electrically charged object.

Like the waves moving along a rope, light waves travel and carry energy. The amount of energy depends on the frequency of the light waves: the higher the frequency, the higher the energy. The frequency of a light wave is also related to the color of the light. For example, blue light has a higher frequency than that of red light. Therefore, a beam of blue light has more energy than an equally intense beam of red light has.

Unlike classical physics, quantum theory also describes light as a particle. Scientists revealed this aspect of light behavior in several experiments performed during the early 20th century. In one experiment, physicists discovered an interaction between light and particles in a metal. They called this interaction the photoelectric effect. In the photoelectric effect, a beam of light shining on a piece of metal makes the metal emit electrons. The light adds energy to the metal’s electrons, giving them enough energy to break free from the metal. If light was made strictly of waves, each electron in the metal could absorb many continuous waves of light and gain more and more energy. Increasing the intensity of the light, or adding more light waves, would add more energy to the emitted electrons. Shining a more and more intense beam of light on the metal would make the metal emit electrons with more and more energy.

Scientists found, however, that shining a more intense beam of light on the metal just made the metal emit more electrons. Each of these electrons had the same energy as that of electrons emitted with low intensity light. The electrons could not be interacting with waves, because adding more waves did not add more energy to the electrons. Instead, each electron had to be interacting with just a small piece of the light beam. These pieces were like little packets of light energy, or particles of light. The size, or energy, of each packet depended only on the frequency, or color, of the light—not on the intensity of the light. A more intense beam of light just had more packets of light energy, but each packet contained the same amount of energy. Individual electrons could absorb one packet of light energy and break free from the metal. Increasing the intensity of the light added more packets of energy to the beam and enabled a greater number of electrons to break free—but each of these emitted electrons had the same amount of energy. Scientists could only change the energy of the emitted electrons by changing the frequency, or color, of the beam. Changing from red light to blue light, for example, increased the energy of each packet of light. In this case, each emitted electron absorbed a bigger packet of light energy and had more energy after it broke free of the metal. Using these results, physicists developed a model of light as a particle, and they called these light particles photons.

In 1922 American physicist Arthur Compton discovered another interaction, now called the Compton effect, that reveals the particle nature of light. In the Compton effect, light collides with an electron. The collision knocks the electron off course and changes the frequency, and therefore energy, of the light. The light affects the electron in the same way a particle with momentum would: It bumps the electron and changes the electron’s path. The light is also affected by the collision as though it were a particle, in that its energy and momentum changes.

Momentum is a quantity that can be defined for all particles. For light particles, or photons, momentum depends on the frequency, or color, of the photon, which in turn depends on the photon’s energy. The energy of a photon is equal to a constant number, called Planck’s constant, times the frequency of the photon. Planck’s constant is named for German physicist Max Planck, who first proposed the relationship between energy and frequency. The accepted value of Planck’s constant is 6.626 × 10^-34 joule-second. This number is very small—written out, it is a decimal point followed by 33 zeroes, followed by the digits 6626. The energy of a single photon is therefore very small.

The dual nature of light seems puzzling because we have no everyday experience with wave-particle duality. Waves are everyday phenomena; we are all familiar with waves on a body of water or on a vibrating rope. Particles, too, are everyday objects—baseballs, cars, buildings, and even people can be thought of as particles. But to our senses, there are no everyday objects that are both waves and particles. Scientists increasingly find that the rules that apply to the world we see are only approximations of the rules that govern the unseen world of light and subatomic particles.

B Matter as Waves and Particles

In 1923 French physicist Louis de Broglie suggested that all particles—not just photons—have both wave and particle properties. He calculated that every particle has a wavelength (represented by λ, the Greek letter lambda) equal to Planck’s constant (h) divided by the momentum (p) of the particle: λ = h/p. Electrons, atoms, and all other particles have de Broglie wavelengths. The momentum of an object depends on its speed and mass, so the faster and heavier an object is, the larger its momentum (p) will be. Because Planck’s constant (h) is an extremely tiny number, the de Broglie wavelength (h/p) of any visible object is exceedingly small. In fact, the de Broglie wavelength of anything much larger than an atom is smaller than the size of one of its atoms. For example, the de Broglie wavelength of a baseball moving at 150 km/h (90 mph) is 1.1 × 10^-34 m (3.6 × 10^-34 ft). The diameter of a hydrogen atom (the simplest and smallest atom) is about 5 × 10^-11 m (about 2 × 10^-10 ft), more than 100 billion trillion times larger than the de Broglie wavelength of the baseball. The de Broglie wavelengths of everyday objects are so tiny that the wave nature of these objects does not affect their visible behavior, so their wave-particle duality is undetectable to us.

De Broglie wavelengths become important when the mass, and therefore momentum, of particles is very small. Particles the size of atoms and electrons have demonstrable wavelike properties. One of the most dramatic and interesting demonstrations of the wave behavior of electrons comes from the double-slit experiment. This experiment consists of a barrier set between a source of electrons and an electron detector. The barrier contains two slits, each about the width of the de Broglie wavelength of an electron. On this small scale, the wave nature of electrons becomes evident, as described in the following paragraphs.

Scientists can determine whether the electrons are behaving like waves or like particles by comparing the results of double-slit experiments with those of similar experiments performed with visible waves and particles. To establish how visible waves behave in a double-slit apparatus, physicists can replace the electron source with a device that creates waves in a tank of water. The slits in the barrier are about as wide as the wavelength of the water waves. In this experiment, the waves spread out spherically from the source until they hit the barrier. The waves pass through the slits and spread out again, producing two new wave fronts with centers as far apart as the slits are. These two new sets of waves interfere with each other as they travel toward the detector at the far end of the tank.

The waves interfere constructively in some places (adding together) and destructively in others (canceling each other out). The most intense waves—that is, those formed by the most constructive interference—hit the detector at the spot opposite the midpoint between the two slits. These strong waves form a peak of intensity on the detector. On either side of this peak, the waves destructively interfere and cancel each other out, creating a low point in intensity. Further out from these low points, the waves are weaker, but they constructively interfere again and create two more peaks of intensity, smaller than the large peak in the middle. The intensity then drops again as the waves destructively interfere. The intensity of the waves forms a symmetrical pattern on the detector, with a large peak directly across from the midpoint between the slits and alternating low points and smaller and smaller peaks on either side.

To see how particles behave in the double-slit experiment, physicists replace the water with marbles. The barrier slits are about the width of a marble, as the point of this experiment is to allow particles (in this case, marbles) to pass through the barrier. The marbles are put in motion and pass through the barrier, striking the detector at the far end of the apparatus. The results show that the marbles do not interfere with each other or with themselves like waves do. Instead, the marbles strike the detector most frequently in the two points directly opposite each slit.

When physicists perform the double-slit experiment with electrons, the detection pattern matches that produced by the waves, not the marbles. These results show that electrons do have wave properties. However, if scientists run the experiment using a barrier whose slits are much wider than the de Broglie wavelength of the electrons, the pattern resembles the one produced by the marbles. This shows that tiny particles such as electrons behave as waves in some circumstances and as particles in others.

C Uncertainty Principle

Before the development of quantum theory, physicists assumed that, with perfect equipment in perfect conditions, measuring any physical quantity as accurately as desired was possible. Quantum mechanical equations show that accurate measurement of both the position and the momentum of a particle at the same time is impossible. This rule is called Heisenberg’s uncertainty principle after German physicist Werner Heisenberg, who derived it from other rules of quantum theory. The uncertainty principle means that as physicists measure a particle’s position with more and more accuracy, the momentum of the particle becomes less and less precise, or more and more uncertain, and vice versa.

Heisenberg formally stated his principle by describing the relationship between the uncertainty in the measurement of a particle’s position and the uncertainty in the measurement of its momentum. Heisenberg said that the uncertainty in position (represented by Δx) times the uncertainty in momentum (represented by Δp;) must be greater than a constant number equal to Planck’s constant (h) divided by 4 ( is a constant approximately equal to 3.14). Mathematically, the uncertainty principle can be written as Δx Δp > h / 4. This relationship means that as a scientist measures a particle’s position more and more accurately—so the uncertainty in its position becomes very small—the uncertainty in its momentum must become large to compensate and make this expression true. Likewise, if the uncertainty in momentum, Δp, becomes small, Δx must become large to make the expression true.

One way to understand the uncertainty principle is to consider the dual wave-particle nature of light and matter. Physicists can measure the position and momentum of an atom by bouncing light off of the atom. If they treat the light as a wave, they have to consider a property of waves called diffraction when measuring the atom’s position. Diffraction occurs when waves encounter an object—the waves bend around the object instead of traveling in a straight line. If the length of the waves is much shorter than the size of the object, the bending of the waves just at the edges of the object is not a problem. Most of the waves bounce back and give an accurate measurement of the object’s position. If the length of the waves is close to the size of the object, however, most of the waves diffract, making the measurement of the object’s position fuzzy. Physicists must bounce shorter and shorter waves off an atom to measure its position more accurately. Using shorter wavelengths of light, however, increases the uncertainty in the measurement of the atom’s momentum.

Light carries energy and momentum, because of its particle nature (described in the Compton effect). Photons that strike the atom being measured will change the atom’s energy and momentum. The fact that measuring an object also affects the object is an important principle in quantum theory. Normally the affect is so small it does not matter, but on the small scale of atoms, it becomes important. The bump to the atom increases the uncertainty in the measurement of the atom’s momentum. Light with more energy and momentum will knock the atom harder and create more uncertainty. The momentum of light is equal to Plank’s constant divided by the light’s wavelength, or p = h/λ. Physicists can increase the wavelength to decrease the light’s momentum and measure the atom’s momentum more accurately. Because of diffraction, however, increasing the light’s wavelength increases the uncertainty in the measurement of the atom’s position. Physicists most often use the uncertainty principle that describes the relationship between position and momentum, but a similar and important uncertainty relationship also exists between the measurement of energy and the measurement of time.

III PROBABILITY AND WAVE FUNCTIONS

Quantum theory gives exact answers to many questions, but it can only give probabilities for some values. A probability is the likelihood of an answer being a certain value. Probability is often represented by a graph, with the highest point on the graph representing the most likely value and the lowest representing the least likely value. For example, the graph that shows the likelihood of finding the electron of a hydrogen atom at a certain distance from the nucleus looks like the following:

The nucleus of the atom is at the left of the graph. The probability of finding the electron very near the nucleus is very low. The probability reaches a definite peak, marking the spot at which the electron is most likely to be.

Scientists use a mathematical expression called a wave function to describe the characteristics of a particle that are related to time and space—such as position and velocity. The wave function helps determine the probability of these aspects being certain values. The wave function of a particle is not the same as the wave suggested by wave-particle duality. A wave function is strictly a mathematical way of expressing the characteristics of a particle. Physicists usually represent these types of wave functions with the Greek letter psi, Ψ. The wave function of the electron in a hydrogen atom is:

The symbol  and the letter e in this equation represent constant numbers derived from mathematics. The letter a is also a constant number called the Bohr radius for the hydrogen atom. The square of a wave function, or a wave function multiplied by itself, is equal to the probability density of the particle that the wave function describes. The probability density of a particle gives the likelihood of finding the particle at a certain point.

The wave function described above does not depend on time. An isolated hydrogen atom does not change over time, so leaving time out of the atom’s wave function is acceptable. For particles in systems that change over time, physicists use wave functions that depend on time. This lets them calculate how the system and the particle’s properties change over time. Physicists represent a time-dependent wave function with Ψ(t), where t represents time.

The wave function for a single atom can only reveal the probability that an atom will have a certain set of characteristics at a certain time. Physicists call the set of characteristics describing an atom the state of the atom. The wave function cannot describe the actual state of the atom, just the probability that the atom will be in a certain state.

The wave functions of individual particles can be added together to create a wave function for a system, so quantum theory allows physicists to examine many particles at once. The rules of probability state that probabilities and actual values match better and better as the number of particles (or dice thrown, or coins tossed, whatever the probability refers to) increases. Therefore, if physicists consider a large group of atoms, the wave function for the group of atoms provides information that is more definite and useful than that provided by the wave function of a single atom.

An example of a wave function for a single atom is one that describes an atom that has absorbed some energy. The energy has boosted the atom’s electrons to a higher energy level, and the atom is said to be in an excited state. It can return to its normal ground state (or lowest energy state) by emitting energy in the form of a photon. Scientists call the wave function of the initial exited state Ψ_i (with “i” indicating it is the initial state) and the wave function of the final ground state Ψ_f (with “f” representing the final state). To describe the atom’s state over time, they multiply Ψ_i by some function, a(t), that decreases with time, because the chances of the atom being in this excited state decrease with time. They multiply Ψ_f by some function, b(t), that increases with time, because the chances of the atom being in this state increase with time. The physicist completing the calculation chooses a(t) and b(t) based on the characteristics of the system. The complete wave equation for the transition is the following:

Ψ = a(t) Ψ_i + b(t) Ψ_f.

At any time, the rules of probability state that the probability of finding a single atom in either state is found by multiplying the coefficient of its wave function (a(t) or b(t)) by itself. For one atom, this does not give a very satisfactory answer. Even though the physicist knows the probability of finding the atom in one state or the other, whether or not reality will match probability is still far from certain. This idea is similar to rolling a pair of dice. There is a 1 in 6 chance that the roll will add up to seven, which is the most likely sum. Each roll is random, however, and not connected to the rolls before it. It would not be surprising if ten rolls of the dice failed to yield a sum of seven. However, the actual number of times that seven appears matches probability better as the number of rolls increases. For one million or one billion rolls of the dice, one of every six rolls would almost certainly add up to seven.

Similarly, for a large number of atoms, the probabilities become approximate percentages of atoms in each state, and these percentages become more accurate as the number of atoms observed increases. For example, if the square of a(t) at a certain time is 0.2, then in a very large sample of atoms, 20 percent (0.2) of the atoms will be in the initial state and 80 percent (0.8) will be in the final state.

One of the most puzzling results of quantum mechanics is the effect of measurement on a quantum system. Before a scientist measures the characteristics of a particle, its characteristics do not have definite values. Instead, they are described by a wave function, which gives the characteristics only as fuzzy probabilities. In effect, the particle does not exist in an exact location until a scientist measures its position. Measuring the particle fixes its characteristics at specific values, effectively “collapsing” the particle’s wave function. The particle’s position is no longer fuzzy, so the wave function that describes it has one high, sharp peak of probability. If the position of a particle has just been measured, the graph of its probability density looks like the following:

In the 1930s physicists proposed an imaginary experiment to demonstrate how measurement causes complications in quantum mechanics. They imagined a system that contained two particles with opposite values of spin, a property of particles that is analogous to angular momentum. The physicists can know that the two particles have opposite spins by setting the total spin of the system to be zero. They can measure the total spin without directly measuring the spin of either particle. Because they have not yet measured the spin of either particle, the spins do not actually have defined values. They exist only as fuzzy probabilities. The spins only take on definite values when the scientists measure them.

In this hypothetical experiment the scientists do not measure the spin of each particle right away. They send the two particles, called an entangled pair, off in opposite directions until they are far apart from each other. The scientists then measure the spin of one of the particles, fixing its value. Instantaneously, the spin of the other particle becomes known and fixed. It is no longer a fuzzy probability but must be the opposite of the other particle, so that their spins will add to zero. It is as though the first particle communicated with the second. This apparent instantaneous passing of information from one particle to the other would violate the rule that nothing, not even information, can travel faster than the speed of light. The two particles do not, however, communicate with each other. Physicists can instantaneously know the spin of the second particle because they set the total spin of the system to be zero at the beginning of the experiment. In 1997 Austrian researchers performed an experiment similar to the hypothetical experiment of the 1930s, confirming the effect of measurement on a quantum system.

IV THE QUANTUM ATOM

The first great achievement of quantum theory was to explain how atoms work. Physicists found explaining the structure of the atom with classical physics to be impossible. Atoms consist of negatively charged electrons bound to a positively charged nucleus. The nucleus of an atom contains positively charged particles called protons and may contain neutral particles called neutrons. Protons and neutrons are about the same size but are much larger and heavier than electrons are. Classical physics describes a hydrogen atom as an electron orbiting a proton, much as the Moon orbits Earth. By the rules of classical physics, the electron has a property called inertia that makes it want to continue traveling in a straight line. The attractive electrical force of the positively charged proton overcomes this inertia and bends the electron’s path into a circle, making it stay in a closed orbit. The classical theory of electromagnetism says that charged particles (such as electrons) radiate energy when they bend their paths. If classical physics applied to the atom, the electron would radiate away all of its energy. It would slow down and its orbit would collapse into the proton within a fraction of a second. However, physicists know that atoms can be stable for centuries or longer.

Quantum theory gives a model of the atom that explains its stability. It still treats atoms as electrons surrounding a nucleus, but the electrons do not orbit the nucleus like moons orbiting planets. Quantum mechanics gives the location of an electron as a probability instead of pinpointing it at a certain position. Even though the position of an electron is uncertain, quantum theory prohibits the electron from being at some places. The easiest way to describe the differences between the allowed and prohibited positions of electrons in an atom is to think of the electron as a wave. The wave-particle duality of quantum theory allows electrons to be described as waves, using the electron’s de Broglie wavelength.

If the electron is described as a continuous wave, its motion may be described as that of a standing wave. Standing waves occur when a continuous wave occupies one of a set of certain distances. These distances enable the wave to interfere with itself in such a way that the wave appears to remain stationary. Plucking the string of a musical instrument sets up a standing wave in the string that makes the string resonate and produce sound. The length of the string, or the distance the wave on the string occupies, is equal to a whole or half number of wavelengths. At these distances, the wave bounces back at either end and constructively interferes with itself, which strengthens the wave. Similarly, an electron wave occupies a distance around the nucleus of an atom, or a circumference, that enables it to travel a whole or half number of wavelengths before looping back on itself. The electron wave therefore constructively interferes with itself and remains stable:

An electron wave cannot occupy a distance that is not equal to a whole or half number of wavelengths. In a distance such as this, the wave would interfere with itself in a complicated way, and would become unstable:

An electron has a certain amount of energy when its wave occupies one of the allowed circumferences around the nucleus of an atom. This energy depends on the number of wavelengths in the circumference, and it is called the electron’s energy level. Because only certain circumferences, and therefore energy levels, are allowed, physicists say that the energy levels are quantized. This quantization means that the energies of the levels can only take on certain values.

The regions of space in which electrons are most likely to be found are called orbitals. Orbitals look like fuzzy, three-dimensional shapes. More than one orbital, meaning more than one shape, may exist at certain energy levels. Electron orbitals are also quantized, meaning that only certain shapes are allowed in each energy level. The quantization of electron orbitals and energy levels in atoms explains the stability of atoms. An electron in an energy level that allows only one wavelength is at the lowest possible energy level. An atom with all of its electrons in their lowest possible energy levels is said to be in its ground state. Unless it is affected by external forces, an atom will stay in its ground state forever.

The quantum theory explanation of the atom led to a deeper understanding of the periodic table of the chemical elements. The periodic table of elements is a chart of the known elements. Scientists originally arranged the elements in this table in order of increasing atomic number (which is equal to the number of protons in the nuclei of each element’s atoms) and according to the chemical behavior of the elements. They grouped elements that behave in a similar way together in columns. Scientists found that elements that behave similarly occur in a periodic fashion according to their atomic number. For example, a family of elements called the noble gases all share similar chemical properties. The noble gases include neon, xenon, and argon. They do not react easily with other elements and are almost never found in chemical compounds. The atomic numbers of the noble gases increase from one element to the next in a periodic way. They belong to the same column at the far right edge of the periodic table.

Quantum theory showed that an element’s chemical properties have little to do with the nucleus of the element’s atoms, but instead depend on the number and arrangement of the electrons in each atom. An atom has the same number of electrons as protons, making the atom electrically neutral. The arrangement of electrons in an atom depends on two important parts of quantum theory. The first is the quantization of electron energy, which limits the regions of space that electrons can occupy. The second part is a rule called the Pauli exclusion principle, first proposed by Austrian-born Swiss physicist Wolfgang Pauli.

The Pauli exclusion principle states that no electron can have exactly the same characteristics as those of another electron. These characteristics include orbital, direction of rotation (called spin), and direction of orbit. Each energy level in an atom has a set number of ways these characteristics can combine. The number of combinations determines how many electrons can occupy an energy level before the electrons have to start filling up the next level.

An atom is the most stable when it has the least amount of energy, so its lowest energy levels fill with electrons first. Each energy level must be filled before electrons begin filling up the next level. These rules, and the rules of quantum theory, determine how many electrons an atom has in each energy level, and in particular, how many it has in its outermost level. Using the quantum mechanical model of the atom, physicists found that all the elements in the same column of the periodic table also have the same number of electrons in the outer energy level of their atoms. Quantum theory shows that the number of electrons in an atom’s outer level determines the atom’s chemical properties, or how it will react with other atoms.

The number of electrons in an atom’s outer energy level is important because atoms are most stable when their outermost energy level is filled, which is the case for atoms of the noble gases. Atoms imitate the noble gases by donating electrons to, taking electrons from, or sharing electrons with other atoms. If an atom’s outer energy level is only partially filled, it will bond easily with atoms that can help it fill its outer level. Atoms that are missing the same number of electrons from their outer energy level will react similarly to fill their outer energy level.

Quantum theory also explains why different atoms emit and absorb different wavelengths of light. An atom stores energy in its electrons. An atom with all of its electrons at their lowest possible energy levels has its lowest possible energy and is said to be in its ground state. One of the ways atoms can gain more energy is to absorb light in the form of photons, or particles of light. When a photon hits an atom, one of the atom’s electrons absorbs the photon. The photon’s energy makes the electron jump from its original energy level up to a higher energy level. This jump leaves an empty space in the original inner energy level, making the atom less stable. The atom is now in an excited state, but it cannot store the new energy indefinitely, because atoms always seek their most stable state. When the atom releases the energy, the electron drops back down to its original energy level. As it does, the electron releases a photon.

Quantum theory defines the possible energy levels of an atom, so it defines the particular jumps that an electron can make between energy levels. The difference between the old and new energy levels of the electron is equal to the amount of energy the atom stores. Because the energy levels are quantized, atoms can only absorb and store photons with certain amounts of energy. The photon’s energy is related to its frequency, or color. As the frequency of photons increases, their energy increases. Atoms can only absorb certain amounts of energy, so only certain frequencies of light can excite atoms. Likewise, atoms only emit certain frequencies of light when they drop to their ground state. The different frequencies available to different atoms help astronomers, for example, determine the chemical makeup of a star by observing which wavelengths are especially weak or strong in the star’s light. See also Spectroscopy.

V DEVELOPMENT OF QUANTUM THEORY

The development of quantum theory began with German physicist Max Planck’s proposal in 1900 that matter can emit or absorb energy only in small, discrete packets, called quanta. This idea introduced the particle nature of light. In 1905 German-born American physicist Albert Einstein used Planck’s work to explain the photoelectric effect, in which light hitting a metal makes the metal emit electrons. British physicist Ernest Rutherford proved that atoms consisted of electrons bound to a nucleus in 1911. In 1913 Danish physicist Niels Bohr proposed that classical mechanics could not explain the structure of the atom and developed a model of the atom with electrons in fixed orbits. Bohr’s model of the atom proved difficult to apply to all but the simplest atoms.

In 1923 French physicist Louis de Broglie suggested that matter could be described as a wave, just as light could be described as a particle. The wave model of the electron allowed Austrian physicist Erwin Schrödinger to develop a mathematical method of determining the probability that an electron will be at a particular place at a certain time. Schrödinger published his theory of wave mechanics in 1926. Around the same time, German physicist Werner Heisenberg developed a way of calculating the characteristics of electrons that was quite different from Schrödinger’s method but yielded the same results. Heisenberg’s method was called matrix mechanics.

In 1925 Austrian-born Swiss physicist Wolfgang Pauli developed the Pauli exclusion principle, which allowed physicists to calculate the structure of the quantum atom for the first time. In 1926 Heisenberg and two of his colleagues, German physicists Max Born and Ernst Pascual Jordan, published a theory that combined the principles of quantum theory with the classical theory of light (called electrodynamics). Heisenberg made another important contribution to quantum theory in 1927 when he introduced the Heisenberg uncertainty principle.

Since these first breakthroughs in quantum mechanical research, physicists have focused on testing and refining quantum theory, further connecting the theory to other theories, and finding new applications. In 1928 British physicist Paul Dirac refined the theory that combined quantum theory with electrodynamics. He developed a model of the electron that was consistent with both quantum theory and Einstein’s special theory of relativity, and in doing so he created a theory that came to be known as quantum electrodynamics, or QED. In the early 1950s Japanese physicist Tomonaga Shin’ichirō and American physicists Richard Feynman and Julian Schwinger each independently improved the scientific community’s understanding of QED and made it an experimentally testable theory that successfully predicted or explained the results of many experiments.

VI CURRENT RESEARCH AND APPLICATIONS

At the turn of the 21st century, physicists were still finding new problems to study with quantum theory and new applications for quantum theory. This research will probably continue for many decades. Quantum theory is technically a fully formulated theory—any questions about the physical world can be calculated using quantum mechanics, but some are too complicated to solve in practice. The attempt to find quantum explanations of gravitation and to find a unified description of all the forces in nature are promising and active areas of research. Researchers try to find out why quantum theory explains the way nature works—they may never find an answer, but the effort to do so is underway. Physicists also study the complicated area of overlap between classical physics and quantum mechanics and work on the applications of quantum mechanics.

Studying the intersection of quantum theory and classical physics requires developing a theory that can predict how quantum systems will behave as they get larger or as the number of particles involved approaches the size of problems described by classical physics. The mathematics involved is extremely difficult, but physicists continue to advance in their research. The constantly increasing power of computers should continue to help scientists with these calculations.

New research in quantum theory also promises new applications and improvements to known applications. One of the most potentially powerful applications is quantum computing. In quantum computing, scientists make use of the behavior of subatomic particles to perform calculations. Making calculations on the atomic level, a quantum computer could theoretically investigate all the possible answers to a query at the same time and make many calculations in parallel. This ability would make quantum computers thousands or even millions of time faster than current computers. Advancements in quantum theory also hold promise for the fields of optics, chemistry, and atomic theory.