Abstract It is commonplace to recount the history of quantum physics on the basis of phenomena that have found no satisfactory explanation in the context of so‐called classical physics. This is the case of, for example, blackbody radiation, the photoelectric effect, specific heats, and series of spectral lines. This story goes in another direction: new knowledge about quantum physics not only emerged from the need to explain new phenomena that conflicted with old theoretical structures, but also from the attempts to provide a quantum explanation of phenomena, like optical dispersion, which for a long time had found a very convincing explanation in old physical models, such as the resonance model. The boundary between classical and quantum domains of knowledge was not fixed a priori, but historically negotiated in the context of specific problems, including the problem of optical dispersion.
Abstract It is commonplace to recount the history of quantum physics on the basis of phenomena that have found no satisfactory explanation in the context of so‐called classical physics. This is the case of, for example, blackbody radiation, the photoelectric effect, specific heats, and series of spectral lines. This story goes in another direction: new knowledge about quantum physics not only emerged from the need to explain new phenomena that conflicted with old theoretical structures, but also from the attempts to provide a quantum explanation of phenomena, like optical dispersion, which for a long time had found a very convincing explanation in old physical models, such as the resonance model. The boundary between classical and quantum domains of knowledge was not fixed a priori, but historically negotiated in the context of specific problems, including the problem of optical dispersion.
Ever splitting the light! How often do they strive to divide that which, despite everything, would always remain single and whole. Goethe (quoted in Zajonc 1993) Introduction The use of electromagnetic wave theory and geometrical optics to describe propagation of light is satisfactory when there is no exchange of energy between radiation and matter. All observable characteristics – direction of propagation, polarization, diffraction, interference, the energy of radiation, and so forth – are accurately described by one of these so-called classical theories. However, with the exception of absorption by lossy media (eqn. 4.36) or the effects of dispersion (eqn. 4.22), classical theories fail to give reasons for many phenomena that have practical consequences in modern technology and that involve interaction between radiation and matter. Even the partially successful descriptions of dispersion or loss cannot explain the existence of the multitude of spectrally distinct absorption lines; cannot predict the wavelengths for absorption or the wavelengths for anomalous dispersion; cannot account for all the absorbed energy; and, most importantly, cannot predict or describe the effect of optical gain, which is closely related to absorption. Thus, the principles of operation of many important devices of modern optics such as lasers, photodiodes, electronic cameras, and television screens cannot be explained by classical theories. Even the emission by the sun or an incandescent lamp are beyond the scope of these theories. It is evident therefore that a new, modern theory is necessary – one that is either more complete than, or simply complements, the classical theories.
Abstract The new quantum mechanics could at first be used to answer questions concerning radiation only through analogies with the classical theory. In Heisenberg’s original matrix theory, for instance, it is assumed that the matrix elements of the polarisation of an atom determine the emission and absorption of radiation analogously to the Fourier components in the classical theory. In more recent theories a certain expression for the electric density obtained from the quantum mechanics is used to determine the emitted radiation by the same formulæ as in the classical theory. These methods give satisfactory results in many cases, but cannot even be applied to problems where the classical analogies are obscure or non-existent, such as resonance radiation and the breadths of spectral lines. A theory of radiation has been given by the author which rests on a more definite basis. It appears that one can treat a field of radiation as a dynamical system, whose interaction with an ordinary atomic system may be described by a Hamiltonian function. The dynamical variables specifying the field are the energies and phases of its various harmonic conrponents, each of which is effectively a simple harmonic oscillator. One must, of course, in the quantum theory take these variables to be q-numbers satisfying the proper quantum conditions. One finds then that the Hamiltonian for the interaction of the field with an atom is of the same form as that for the interaction of an assembly of light-quanta with the atom. There is thus a complete formal reconciliation between the wave and light-quantum points of view.
From a historical point of view, a distinction can be drawn between ‘old quantum theory’ and the full quantum theory that we now use. Old quantum theory was in essence a patchwork, cobbled together by incorporating some quantum ideas into essentially classical physics. The work of Planck, Einstein, Bohr, and Sommerfeld can be bracketed as old quantum theory. This classification is not meant to undermine the tremendous achievement that old quantum theory represents, but simply to underline its standing as a stage on the way to a fully formed quantum theory, which emerged from the work of Heisenberg, Schrodinger, Born, and Dirac. The development of the photon concept is a key example of a radically new idea gradually gaining acceptance. The process works via a growing realization that more and more things can be explained in the context of the photon model.
Introduction While it might appear that the nineteenth-century physics presented in this chapter has no place in a topic as quantum mechanically oriented as atomic physics, this is simply not the case. The purpose of this first chapter is to try to convince the readers that the material learned in their early years of studying physics is not disjoint from modern topics, but in fact can provide a foundation for their further understanding. Other examples will occur later. The reader may be a bit surprised to see that the results of the classical description turn out to be so close to the quantum mechanical results. Where there are significant disagreements between classical and quantum descriptions, it is necessary to explain why these occur. The correspondence principle requires that in the limit of large quantum numbers the complete quantum mechanical description must agree with the classical one. It is always better to need fewer of these explanations and to be able to treat physics as a coherent whole instead of a collection of topics. The consequences of classical physics are intuitively familiar, and this is often most helpful in gaining deeper understanding. In fact, the approach taken in very many of the chapters in this book is to start with a purely classical description of a topic, and then transport it directly into the Schrödinger equation. Radiation from an accelerated charge, as treated here in the harmonic case, provides an ideal setting for such pedagogy. Even though classical mechanics is used in place of quantum mechanics, for the case of harmonic motion, the results are quite compatible. The early history of atomic physics contains many topics that are well worth reading about, especially the experimental facilities. For example, there were no electric motors, wire was not readily available, and making even a crude vacuum was an experimental tour de force. Very many textbooks have discussions of these topics, and so they will not be presented here. But the reader is warned that certain oft-repeated modern descriptions are simply wrong. Perhaps the most important notion to be gained from this chapter is that the classical description of a harmonically bound electron provides quite accurate results about the interaction between atoms and light. Of course, the utility of this description is limited because the classical harmonic oscillator has no internal structure, is infinitely deep, and has a continuous energy spectrum.
This chapter begins with a brief outline of some of the key motivations for considering a quantum theory: the early attempts to determine the spectral distribution of energy density of black bodies; stability of atoms and molecules; specific heats of solids; interference and diffraction of light beams; polarization of photons. The experimental foundations of wave mechanics are then presented in detail, but in a logical order quite different from its historical development: photo-emission of electrons by metallic surfaces, X- and γ-ray scattering from gases, liquids and solids, interference experiments, atomic spectra and the Bohr hypotheses, the experiment of Franck and Hertz, the Bragg experiment, diffraction of electrons by a crystal of nickel (Davisson and Germer), and measurements of position and velocity of an electron. The need for a quantum theory In the second half of the nineteenth century it seemed that the laws of classical mechanics, developed by the genius of Newton, Lagrange, Hamilton, Jacobi and Poincaré, the Maxwell theory of electromagnetic phenomena and the laws of classical statistical mechanics could account for all known physical phenomena. Still, it became gradually clear, after several decades of experimental and theoretical work, that one has to formulate a new kind of mechanics, which reduces to classical mechanics in a suitable limit, and makes it possible to obtain a consistent description of phenomena that cannot be understood within the classical framework. It is now appropriate to present a brief outline of this new class of phenomena, the systematic investigation of which is the object of the following sections and of chapters 4 and 14.