It is demonstrated that, if one remains in the framework of quantum mechanics taken alone, stationary states (energy eigenstates) are in no way singled out with respect to nonstationary ones, and moreover the stationary states would be difficult if possible to realize in practice. Owing to the nonstationary states any quantum system can absorb or emit energy in arbitrary continuous amounts. The peculiarity of the stationary states appears only if electromagnetic radiation that must always accompany nonstationary processes in real systems is taken into account. On the other hand, when the quantum system absorbs or emits energy in the form of a wave the determining role is played by resonance interaction of the system with the wave. Here again the stationary states manifest themselves. These facts and influence of the resonator upon the incident wave enable one to explain all effects ascribed to manifestation of the corpuscular properties of light (the photoelectric effect, the Compton effect etc.) solely on a base of the wave concept of light.
It is demonstrated that, if one remains in the framework of quantum mechanics taken alone, stationary states (energy eigenstates) are in no way singled out with respect to nonstationary ones, and moreover the stationary states would be difficult if possible to realize in practice. Owing to the nonstationary states any quantum system can absorb or emit energy in arbitrary continuous amounts. The peculiarity of the stationary states appears only if electromagnetic radiation that must always accompany nonstationary processes in real systems is taken into account. On the other hand, when the quantum system absorbs or emits energy in the form of a wave the determining role is played by resonance interaction of the system with the wave. Here again the stationary states manifest themselves. These facts and influence of the resonator upon the incident wave enable one to explain all effects ascribed to manifestation of the corpuscular properties of light (the photoelectric effect, the Compton effect etc.) solely on a base of the wave concept of light.
An attempt is made to present a consistent detailed theory of optical phenomena, based on the suggestion recently made by the author in collaboration with Bohr and Kramers. This suggestion is that atoms are radiating or absorbing continuously, during their stationary states, and that transitions influence radiation only in terminating the radiation characteristic of the old state, and substituting that of the new. The atoms, on the other hand, are supposed not to change their energy while radiating, but to change it discontinuously on transition. This necessitates giving up the detailed application of the conservation of energy in interaction between atoms and radiation. In the present paper, an additional suggestion is made, namely that resonance radiation is to be identified with the radiation carried out by the spherical wavelets which, by their interference with the external field, also produce absorption. This is practically a return to the classical picture of resonance radiation. Statement of the theory consists formally of two parts: the description of the behavior of atoms, and of radiation, when the two interact. The first involves the statement of the probabilities of transition of atoms, and is taken without change from Einstein. The probability of interruption of coherent vibrations is also discussed. The second requires the specification of the fields emitted by atoms in any steady state under the influence of any external field. These consist of spherical wavelets of the frequencies of the various quantum lines which the atom can emit or absorb in the stationary state in which it is. For emission frequencies, wavelets are emitted even in the absence of an external field; for absorption frequencies, external fields induce wavelets, similar to the wavelets of linearly bound electrons in electron theory, which on the one hand interfere with the external field to produce the phenomena of dispersion, etc., and on the other carry out the resonance radiation in all directions. Detailed descriptions of these fields are given. In a discussion of the theory, it is first shown that the assumptions which have been made about the field satisfy the correspondence principle, in that for large quantum numbers the field aproaches that which would be emitted classically on account of the interaction of an external field and a multiply periodic atom. On the other hand, it is shown that the field has a character essentially like that of classical electron theory, which is known to be in general agreement with experiments. Next, the energy and momentum relations at interaction of atoms and light are investigated, and it is shown that, although these quantities are not precisely conserved, still the assumptions as to atomic and radiation processes have been so made that they are conserved on an average over a great number of atomic processes. Finally the spectral resolution of emitted and absorbed radiation is considered; the theory gives a minimum breadth for the lines, depending on the finite length of wave trains resulting from the finite life in stationary states, and it is shown that Kirchhoff's law is obeyed, the emission and absorption lines being of the same breadth. By way of illustration, specific application of the theory is made to the simple examples of emission of light by bombardment of electrons at the resonance potential, resonance radiation, its quenching by presence of foreign gases, absorption, scattering, and disperison.
Light occupies a special position in our attempts to understand nature both classically and quantum mechanically. We recall that Newton, who made so many fundamental contributions to optics, championed a particle description of light and was not favorably disposed to the wave picture of light. However, the beautiful unification of electricity and magnetism achieved by Maxwell clearly showed that light was properly understood as the wave-like undulations of electric and magnetic fields propagating through space. The central role of light in marking the frontiers of physics continues on into the twentieth century with the ultraviolet catastrophe associated with black-body radiation on the one hand and the photoelectric effect on the other. Indeed, it was here that the era of quantum mechanics was initiated with Planck's introduction of the quantum of action that was necessary to explain the black-body radiation spectrum. The extension of these ideas led Einstein to explain the photoelectric effect, and to introduce the photon concept. It was, however, left to Dirac to combine the wave-and particlelike aspects of light so that the radiation field is capable of explaining all interference phenomena and yet shows the excitation of a specific atom located along a wave front absorbing one photon of energy. In this chapter, following Dirac, we associate each mode of the radiation field with a quantized simple harmonic oscillator, this is the essence of the quantum theory of radiation.
The photoelectric effect, the Compton effects, and now anticorrelation experiments have been claimed to prove that light consists of particles flying through a void. However the particle model is decisively falsified by the known wave qualities of electromagnetic radiation. Quantum Electrodynamics also uses spreading wave amplitudes; not flying particles. The evidence indicates that light is a wave and electrons are electromagnetic wave-structures that absorb and emit light in discrete wave-packets. These wave-quanta are emitted directionally and then spread in space in proportion to their wavelength. Their waves superposition with all other waves in space. In low intensity experiments, the waves that an electron in a photodetector absorbs come from the superpositioning of the source wave-quanta and background radiation. The importance of background radiation is evidenced by "dark counts". Treating electrons and the quanta they absorb and emit as particles when they are composed of waves is the source of all the paradoxes, unreality and confusion in Quantum Mechanics. The word "photon" should be replaced by "quantum" in the description of this particular electronic process. The conceptual model presented here explains the known phenomena without producing paradoxes and unifies quantum and classical electromagnetics.
Classical mechanics, which gives a fairly accurate description of large systems (e.g., solar system) as also of mechanical systems in our every day life, however, breaks down when applied to small (microscopic) systems such as molecules, atoms and nuclei. For example, (1) classical mechanics cannot even explain why the atoms are stable at all. A classical atom with electrons moving in circular or elliptic orbits around the nucleus would continuously radiate energy in the form of electromagnetic radiation because an accelerated charge does radiate energy. As a result the radius of the orbit would become smaller and smaller, resulting in instability of the atom. On the other hand, the atoms are found to be remarkably stable in practice. (2) Another fact of observation that classical mechanics fails to explain is wave particle duality in radiation as well as in material particles. It is well known that light exhibits the phenomena of interference, diffraction and polarization which can be easily understood on the basis of wave aspect of radiation. But light also exhibits the phenomena of photo-electric effect, Compton effect and Raman effect which can only be understood in terms of corpuscular or quantum aspect of radiation. The dual behavior of light, or radiation cannot be consistently understood on the basis of classical concepts alone or explained away by saying that light behaves as wave or particle depending on the kind of experiment we do with it (complementarity). Moreover, a beam of material particles, like electrons and neutrons, demonstrates wave-like properties (e.g., diffraction). A brief outline of phenomena that require quantum mechanics for their understanding follows.
The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed mch (m=massoftheparticle). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.