This paper proposes a fundamentally new approach to the study of stationary states in atoms, which is based on the analysis of the energy of electric and magnetic fields. The circulation of the electromagnetic field in the stationary states of the atom was discovered and the mechanism of optical transitions due to the continuous change of the circulating energy was clarified. The difference between circulating energy flows in the initial and final states is emitted (or absorbed) in the form of a quantum of light. A universal relation for determining the lifetime of excited states is proposed.
This paper proposes a fundamentally new approach to the study of stationary states in atoms, which is based on the analysis of the energy of electric and magnetic fields. The circulation of the electromagnetic field in the stationary states of the atom was discovered and the mechanism of optical transitions due to the continuous change of the circulating energy was clarified. The difference between circulating energy flows in the initial and final states is emitted (or absorbed) in the form of a quantum of light. A universal relation for determining the lifetime of excited states is proposed.
The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is [Formula: see text]. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.
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.
Abstract The principles of the quantum are, as is well known, not compatible with classical dynamics and electrodynamics, nor, indeed, with the extended dynamics and electrodynamics of the theory of relativity, although they do not appear to violate the principles of the theory of relativity themselves. The chief hypothesis of the quantum theory, and the one which is most at variance with classical theories, is the hypothesis of stationary states, and this is so well established by experimental evidence that it can hardly be doubted that some parts of the classical electrodynamics, at any rate, will have to be given up or modified. In the present communication, a more general form of the postulate, put fonvard by the writer some years ago, will be described, which facilitates the application of the quantum theory to problems such as that of the Zeeman phenomenon, involving magnetic fields, and restricts the region within which the classical and quantum theories are in conflict. The postulates of the quantum theory, in its present state, are as follows:— (i) Atoms, or other systems contemplated by the quantum theory, can only exist normally in one or other of certain states called stationary states. While in one of its stationary states the atom does not emit or absorb energy. This is the chief postulate of Bohr’s theory of spectra.
We investigate in this chapter the general problem of the interaction of an atom (or a molecule) and a classical electromagnetic field. Its importance derives firstly from the fact that a large part of our knowledge of atoms is obtained from a study of the radiation they absorb or emit (we shall consider equally visible radiation and radio-frequency and X-rays) and, secondly, that the interaction with matter modifies the propagation of the electromagnetic field itself, notably through absorption, refraction or scattering. The interactions of atoms with light therefore encompass a vast range of physical effects that we could not hope to cover adequately in a single chapter. In this chapter we shall therefore present the fundamental features of the interaction of an atom, which will be treated quantum mechanically, with a classical electromagnetic field, that is an electromagnetic field described by real electric and magnetic vectors obeying Maxwell's equations. A rigorous description of the atom–light interaction would have to take into account the quantum nature of light. This we shall leave to Chapter 6. It turns out, nevertheless, that many important results can be obtained from the semi-classical viewpoint adopted here (although it is perhaps more appropriate to refer to this treatment as ‘semi-quantized’).
In many practical cases a stationary system is perturbed in some way, inducing it to undergo transitions between the otherwise stationary states. Perhaps the best example concerns the radiative transitions of atomic electrons in which the disturbance of an external electromagnetic field causes the electrons to jump between energy levels, emitting or absorbing photons. Equation is a statement of the classical law of conservation of energy. The stimulated emission and absorption of radiation both have close classical analogues. If a simple harmonic oscillator is driven by a sinusoidal electromagnetic field it can gain or lose energy depending on phase angles. The existence of spontaneous emission implies that all excited states of electrical systems are unstable and will eventually decay to the ground state by photon emission. Quantum systems thus comply with the fundamental principle that physical systems tend to seek out their state of lowest energy and maximum entropy.