Quantum Theory

I

Introduction

Quantum Theory, also quantum mechanics, in physics, a theory based on using the concept of the quantum unit to describe the dynamic properties of subatomic particles and the interactions of matter and radiation. The foundation was laid by the German physicist Max Planck, who postulated in 1900 that energy can be emitted or absorbed by matter only in small, discrete units called quanta. Also fundamental to the development of quantum mechanics was the uncertainty principle, formulated by the German physicist Werner Heisenberg in 1927, which states that the position and momentum of a subatomic particle cannot be specified simultaneously.

II

Early History

In the 18th and 19th centuries, Newtonian, or classical, mechanics appeared to provide a wholly accurate description of the motions of bodies—such as, for example, planetary motion. In the late 19th and early 20th centuries, however, experimental findings raised doubts about the completeness of Newtonian theory. Among the newer observations were the lines that appear in the spectra of light emitted by heated gases, or by gases in which electric discharges take place. From the model of the atom developed in the early 20th century by the New Zealand-born physicist Ernest Rutherford, in which negatively charged electrons circle a positive nucleus in orbits prescribed by Newton's laws of motion, scientists had also expected that the electrons would emit light over a broad frequency range, rather than in the narrow frequency ranges that form the lines in a spectrum.

Another puzzle for physicists was the coexistence of two theories of light: the corpuscular theory, which explains light as a stream of particles, and the wave theory, which views light as electromagnetic waves. A third problem was the absence of a molecular basis for thermodynamics. In his book Elementary Principles in Statistical Mechanics (1902), the American mathematical physicist J. Willard Gibbs conceded the impossibility of framing a theory of molecular action that embraced the phenomena of thermodynamics, radiation, and electrical phenomena as they were then understood.

III

Planck's Introduction of the Quantum

At the turn of the century, physicists did not yet clearly recognize that these and other difficulties in physics were in any way related. The first development that led to the solution of these difficulties was Planck's introduction of the concept of the quantum, as a result of physicists' studies of blackbody radiation during the closing years of the 19th century. (The term blackbody refers to an ideal body or surface that absorbs all radiant energy without any reflection.) A body at a moderately high temperature—a “red heat”—gives off most of its radiation in the low-frequency (red and infrared) regions; a body at a higher temperature—”white heat”—gives off comparatively more radiation at higher frequencies (yellow, green, or blue). During the 1890s physicists conducted detailed quantitative studies of these phenomena and expressed their results in a series of curves or graphs. The classical, or prequantum, theory predicted an altogether different set of curves from those actually observed. What Planck did was to devise a mathematical formula that described the curves exactly; he then deduced a physical hypothesis that could explain the formula. His hypothesis was that energy is radiated only in quanta of energy hu, where u is the frequency and h is the quantum of action, now known as Planck's constant.

IV

Einstein's Contribution

The next important developments in quantum mechanics were the work of Albert Einstein. He used Planck's concept of the quantum to explain certain properties of the photoelectric effect—an experimentally observed phenomenon in which electrons are emitted from metal surfaces when radiation falls on these surfaces.

According to classical theory, the energy, as measured by the voltage of the emitted electrons, should be proportional to the intensity of the radiation. Actually, however, the energy of the electrons was found to be independent of the intensity of radiation—which determined only the number of electrons emitted—and to depend solely on the frequency of the radiation. The higher the frequency of the incident radiation, the greater is the electron energy; below a certain critical frequency no electrons are emitted. These facts were explained by Einstein by assuming that a single quantum of radiant energy ejects a single electron from the metal. The energy of the quantum is proportional to the frequency, and so the energy of the electron depends on the frequency.