QUANTUM MECHANICS

science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituentselectrons, protons, neutrons, and other more esoteric particles such as quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X rays, and gamma rays). The behaviour of matter and radiation on the atomic scale often seems peculiar, and the consequences of quantum theory are accordingly difficult to understand and to believe. Its concepts frequently conflict with common-sense notions derived from observations of the everyday world. There is no reason, however, why the behaviour of the atomic world should conform to that of the familiar, large-scale world. It is important to realize that quantum mechanics is a branch of physics and that the business of physics is to describe and account for the way the worldon both the large and the small scaleactually is and not how one imagines it or would like it to be. The study of quantum mechanics is rewarding for several reasons. First, it illustrates the essential methodology of physics. Second, it has been enormously successful in giving correct results in practically every situation to which it has been applied. There is, however, an intriguing paradox. In spite of the overwhelming practical success of quantum mechanics, the foundations of the subject contain unresolved problemsin particular, problems concerning the nature of measurement. An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it; the detailed nature of this disturbance and the exact point at which it occurs are obscure and controversial. Thus, quantum mechanics has attracted some of the ablest scientists of the 20th century, and they have erected what is perhaps the finest intellectual edifice of the period. the branch of mathematical physics that deals with atomic and subatomic systems and their interaction with radiation in terms of observable quantities. It is an outgrowth of the concept that all forms of energy are released in discrete units or bundles called quanta. Quantum mechanics is concerned with phenomena that are so small-scale that they cannot be described in classical terms. Throughout the 1800s most physicists regarded Isaac Newton's dynamical laws as sacrosanct, but it became increasingly clear during the early years of the 20th century that many phenomena, especially those associated with radiation, defy explanation by Newtonian physics. It has come to be recognized that the principles of quantum mechanics rather than those of classical mechanics must be applied when dealing with the behaviour of electrons and nuclei within atoms and molecules. Although conventional quantum mechanics makes no pretense of describing completely what occurs inside the atomic nucleus, it has helped scientists to better understand many processes such as the emission of alpha particles and photodisintegration. Moreover, the field theory of quantum mechanics has provided insight into the properties of mesons and other subatomic particles associated with nuclear phenomena. In the equations of quantum mechanics, Max Planck's constant of action h = 6.626 10-34 joule-second plays a central role. This constant, one of the most important in all of physics, has the dimensions energy time. The term small-scale used to delineate the domain of quantum mechanics should not be literally interpreted as necessarily relating to extent in space. A more precise criterion as to whether quantum modifications of Newtonian laws are important is whether or not the phenomenon in question is characterized by an action (i.e., time integral of kinetic energy) that is large compared to Planck's constant. Accordingly, if a great many quanta are involved, the notion that there is a discrete, indivisible quantum unit loses significance. This fact explains why ordinary physical processes appear to be so fully in accord with the laws of Newton. The laws of quantum mechanics, unlike Newton's deterministic laws, lead to a probabilistic description of nature. As a consequence, one of quantum mechanics' most important philosophical implications concerns the apparent breakdown, or at least a drastic reinterpretation, of the causality principle in atomic phenomena. The history of quantum mechanics may be divided into three main periods. The first began with Planck's theory of black-body radiation in 1900; it may be described as the period in which the validity of Planck's constant was demonstrated but its real meaning was not fully understood. The second period began with the quantum theory of atomic structure and spectra proposed by Niels Bohr in 1913. Bohr's ideas gave an accurate formula for the frequency of spectral lines in many cases and were an enormous help in the codification and understanding of spectra. Nonetheless, they did not represent a consistent, unified theory, constituting as they did a sort of patchwork affair in which classical mechanics was subjected to a somewhat extraneous set of so-called quantum conditions that restrict the constants of integration to particular values. True quantum mechanics appeared in 1926, reaching fruition nearly simultaneously in a variety of formsnamely, the matrix theory of Max Born and Werner Heisenberg, the wave mechanics of Louis V. de Broglie and Erwin Schrdinger, and the transformation theory of P.A.M. Dirac and Pascual Jordan. These different formulations were in no sense alternative theories; rather, they were different aspects of a consistent body of physical law. Additional reading Several book-length studies have been written on the historical development of quantum mechanics; especially noteworthy are Olivier Darrigol, From C-Numbers to Q-Numbers: The Classical Analogy in the History of Quantum Theory (1992); and Max Jammer, The Conceptual Development of Quantum Mechanics, 2nd ed. (1989).Careful historical and philosophical studies of the work of many of the early architects of quantum theory may be found in Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity, 18941912 (1978, reprinted 1987); Bruce R. Wheaton, The Tiger and the Shark: Empirical Roots of Wave-Particle Dualism (1983, reissued 1991); Abraham Pais, Subtle Is the Lord...: The Science and Life of Albert Einstein (1982), and Niels Bohr's Times: In Physics, Philosophy, and Polity (1991); Arthur Fine, The Shaky Game: Einstein, Realism, and the Quantum Theory, 2nd ed. (1996); Max Dresden, H.A. Kramers: Between Tradition and Revolution (1987); David C. Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (1992); Walter Moore, Schrdinger: Life and Thought (1989); and Dugald Murdoch, Niels Bohr's Philosophy of Physics (1987, reissued 1990). The birth of quantum theory in the period 190026, primarily within German university circles, is nicely contextualized by Christa Jungnickel and Russell McCormmach, Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, 2 vol. (1986, reissued 1990). The transition from nonrelativistic quantum mechanics to renormalized quantum electrodynamics over the period 192649 is traced by Silvan S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (1994).There are a number of excellent texts on quantum mechanics at the undergraduate and graduate level. The following is a selection, beginning with the more elementary: A.P. French and Edwin F. Taylor, An Introduction to Quantum Physics (1978); Alastair I.M. Rae, Quantum Mechanics, 2nd ed. (1986); Richard L. Liboff, Introductory Quantum Mechanics, 2nd ed. (1992); Eugen Merzbacher, Quantum Mechanics, 2nd ed. (1970); J.J. Sakurai, Modern Quantum Mechanics, rev. ed. (1994); and Anthony Sudbery, Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians (1986), rather mathematical but including useful accounts and summaries of quantum metaphysics. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, vol. 3, Quantum Mechanics (1965), is a personal and stimulating look at the subject. A good introduction to quantum electrodynamics is Richard P. Feynman, QED: The Strange Theory of Light and Matter (1985).J.C. Polkinghorne, The Quantum World (1984); John Gribbin, In Search of Schrdinger's Cat: Quantum Physics and Reality (1984); Heinz R. Pagels, The Cosmic Code: Quantum Physics as the Language of Nature (1982); and David Z. Albert, Quantum Mechanics and Experience (1992), are all highly readable and instructive books written at a popular level. Bernard d'Espagnat, Conceptual Foundations of Quantum Mechanics, 2nd ed. (1976), is a technical account of the fundamental conceptual problems involved. The proceedings of a conference, New Techniques and Ideas in Quantum Measurement Theory, ed. by Daniel M. Greenberger (1986), contain a wide-ranging set of papers that deal with both the experimental and theoretical aspects of the measurement problem.Applications are presented by H. Haken and H.C. Wolf, Atomic and Quantum Physics: An Introduction to the Fundamentals of Experiment and Theory, 2nd enlarged ed. (1987; originally published in German, 2nd rev. and enlarged ed., 1983); Emilio Segr, Nuclei and Particles: An Introduction to Nuclear and Subnuclear Physics, 2nd rev. and enlarged ed. (1977, reissued 1980); Donald H. Perkins, Introduction to High Energy Physics, 3rd ed. (1987); Charles Kittel, Introduction to Solid State Physics, 6th ed. (1986); and Rodney Loudon, The Quantum Theory of Light, 2nd ed. (1983). B.W. Petley, The Fundamental Physical Constants and the Frontier of Measurement (1985), gives a good account of present knowledge of the fundamental constants. Gordon Leslie Squires The Editors of the Encyclopdia Britannica The interpretation of quantum mechanics Although quantum mechanics has been applied to problems in physics with great success, some of its ideas seem strange. A few of their implications are considered here. The electron: wave or particle? Figure 5: (A) Monochromatic light incident on a pair of slits gives interference fringes (alternate Figure 5: (A) Monochromatic light incident on a pair of slits gives interference fringes (alternate Figure 5: (A) Monochromatic light incident on a pair of slits gives interference fringes (alternate Young's aforementioned experiment in which a parallel beam of monochromatic light is passed through a pair of narrow parallel slits (Figure 5A) has an electron counterpart. In Young's original experiment, the intensity of the light varies with direction after passing through the slits (Figure 5B). The intensity oscillates because of interference between the light waves emerging from the two slits, the rate of oscillation depending on the wavelength of the light and the separation of the slits. The oscillation creates a fringe pattern of alternating light and dark bands that is modulated by the diffraction pattern from each slit. If one of the slits is covered, the interference fringes disappear, and only the diffraction pattern (shown as a broken line in Figure 5B) is observed. Young's experiment can be repeated with electrons all with the same momentum. The screen in the optical experiment is replaced by a closely spaced grid of electron detectors. There are many devices for detecting electrons; the most common are scintillators. When an electron passes through a scintillating material, such as sodium iodide, the material produces a light flash which gives a voltage pulse that can be amplified and recorded. The pattern of electrons recorded by each detector is the same as that predicted for waves with wavelengths given by the Broglie formula. Thus, the experiment provides conclusive evidence for the wave behaviour of electrons. Figure 5: (A) Monochromatic light incident on a pair of slits gives interference fringes (alternate If the experiment is repeated with a very weak source of electrons so that only one electron passes through the slits, a single detector registers the arrival of an electron. This is a well-localized event characteristic of a particle. Each time the experiment is repeated, one electron passes through the slits and is detected. A graph plotted with detector position along one axis and the number of electrons along the other looks exactly like the oscillating interference pattern in Figure 5B. Thus, the intensity function in the figure is proportional to the probability of the electron moving in a particular direction after it has passed through the slits. Apart from its units, the function is identical to Y2, where Y is the solution of the time-independent Schrdinger equation for this particular experiment. If one of the slits is covered, the fringe pattern disappears and is replaced by the diffraction pattern for a single slit. Thus, both slits are needed to produce the fringe pattern. However, if the electron is a particle, it seems reasonable to suppose that it passed through only one of the slits. The apparatus can be modified to ascertain which slit by placing a thin wire loop around each slit. When an electron passes through a loop, it generates a small electric signal, showing which slit it passed through. However, the interference fringe pattern then disappears, and the single-slit diffraction pattern returns. Since both slits are needed for the interference pattern to appear and since it is impossible to know which slit the electron passed through without destroying that pattern, one is forced to the conclusion that the electron goes through both slits at the same time. In summary, the experiment shows both the wave and particle properties of the electron. The wave property predicts the probability of direction of travel before the electron is detected; on the other hand, the fact that the electron is detected in a particular place shows that it has particle properties. Therefore, the answer to the question whether the electron is a wave or a particle is that it is neither. It is an object exhibiting either wave or particle properties, depending on the type of measurement that is made on it. In other words, one cannot talk about the intrinsic properties of an electron; instead, one must consider the properties of the electron and measuring apparatus together.