Quantum Theory

QUANTUM THEORY. A quantum (from the Latin quantum-a definite amount) is a concept characterizing the discontinuity of interactions between elementary particles of matter-electrons, protons, atoms, and molecules-among themselves and with light. The concept of a quantum was introduced by M. Planck (1900) in connection with the theory of radiation of a heated absolutely black body. To explain the distribution of energy over wavelengths in the spectrum of a black body, it is necessary to assume that the absorption and emission of light in matter occur only in whole amounts-quanta-of magnitude hv (v is the frequency of the emitted or absorbed light oscillations, h is a constant always and under all conditions, equal to 6.55 × 10^-27 erg./sec.). In connection with this, Einstein (1905) suggested that even during the propagation of light, the energy of the latter is concentrated in certain centers, light quanta, characterized by energy hv and momentum - (e is the speed of light). This hypothesis, fully consistent with the necessity of the discontinuity of absorption and emission, at the same time leads to extremely important conclusions regarding the actions of light. If a light quantum collides with an electron, then in the general case the result of the collision should be analogous to what happens when two elastic balls collide: the electron and the quantum will fly apart from each other with changed energy and direction. But in the expression for the energy of a quantum, h is always constant; consequently, when the energy of a quantum changes, its frequency v or the corresponding wavelength must change. Applying the laws of conservation of energy and momentum to the process of collision of an electron and a quantum, one can find that the wavelength of light scattered by electrons is 2ft A-*o + ; sinSr :ч тс ' ~ 2 here A₀ is the wavelength of light before scattering, m is the mass of the electron, c is the speed of light, θ is the angle formed by the directions of the quantum before and after scattering. From (1) it is seen that the wavelength of the scattered light is greater than that of the incident light. This increase in the scattered wave must be quite noticeable for rays with a large quantum, i.e., with a large frequency v, for example, for X-rays. Compton first derived consequence (1) from the hypothesis of light quanta and confirmed it experimentally. The lengthening of the wavelength during the scattering of X-rays in a substance must, among other things, have essential significance for understanding the therapeutic action of X-rays. Light atoms, of which living tissue is composed, absorb hard X-rays only to a negligible extent; but as the rays pass through a material medium, they are scattered, undergo multiple Compton lengthening of the wave, become 'softer,' large quanta are, so to speak, exchanged for smaller ones, and thus act on the tissue. If during the absorption of light during an 'inelastic' collision of a quantum with an electron, the energy of the quantum is transferred to the electron, which flies out of the atom, then by the law of conservation of energy the kinetic energy of the flying electron - = /»» (2). This consequence is fully confirmed in the so-called photoelectric effect, when electrons are ejected from matter under the action of light (in this case the part of energy expended by the electron before passing through the surface is taken into account). The hypothesis of light quanta also determines the basic law of the chemical action of light. For the simplest reaction of dissociation of any molecule into its constituent parts, it is necessary that each dissociating molecule absorb 1 quantum. Denoting by E the total energy of monochromatic light absorbed by such a dissociating medium, we find that the number of decomposed molecules This consequence (the so-called Einstein law) is exactly confirmed by experiment. Apparent deviations from it are explained by secondary chemical reactions, complicating the original purely photochemical process. The quantum nature of radiation is also revealed in biological phenomena. For example, the optimal threshold of visual irritation, i.e., the minimum amount of energy of green light (per second) necessary for the appearance of a sensation of light, is measured by several quanta of green light. In the bactericidal action of X-rays, as experiments by Darier show, it is necessary and sufficient for the energy of 1 quantum to kill an organism. Thus, the actions of light give a solid experimental basis to the doctrine of light quanta. At the same time, optical phenomena of interference, diffraction, and polarization testify no less convincingly to the wave nature of light. Consequently, light has to be ascribed simultaneously discontinuous quantum and continuous wave properties. However, the discontinuous quantum character of interactions is inherent not only in light but also in matter. The study of line spectra emitted by atoms led Bohr (1913) to the establishment of the following two postulates, fully confirmed by experiment in various fields: 1) electrons in an atom can exist only in certain stable, stationary states (rotate along certain orbits), forming a discontinuous infinite series and depending on whole numbers and the quantum constant h; 2) during the transition of an electron in an atom or molecule from one stationary state to another, during the absorption or emission of light, the energy of the initial state E_t and the final E_k are related by the relation E_t-E_k-hp

(4). Condition (4) and the mathematical formulation of the first postulate lead to an exact explanation of the regularities in spectra and form the basis of the modern doctrine of the structure of atoms and molecules. The theory of Bohr, however, cannot be considered as finished and perfect. To apply it to specific problems of atomic mechanics, one has to use fairly arbitrary positions of classical mechanics, establishing a somewhat indefinite correspondence between classical and quantum physics. In some problems (for example, the structure of the helium atom), the theory of Bohr led to obviously erroneous results. Thus, the need for a more consistent theory of quanta, uniting light quanta and quantum laws in matter and simultaneously clarifying the relations between classical and quantum laws, became clear. The first very successful attempts to create such a unified theory of quanta belong to de Broglie, Heisenberg, and Schrodinger. The basic idea of the new quantum mechanics is de Broglie's idea of wave mechanics. Just as in the doctrine of light, geometric, ray optics is only the first approximation of true wave optics, so in mechanics, according to de Broglie's idea, classical Newtonian mechanics is only the first approximation of true wave mechanics. In optics, the wave nature of light is revealed in diffraction phenomena, when light has to pass through small holes, near edges, or past small bodies; exactly the same, the wave character of true mechanics begins to manifest itself in the field of micro-phenomena, in atomic and electronic processes. According to de Broglie, every elementary particle, i.e., an electron, a proton, a light quantum, is always accompanied by special 'phase' waves, not carrying energy, the length of which λ = A

(5) (m is the mass of the particle, v is the speed), and the speed of propagation «-£

₍6) (c is the speed of light). The idea of such waves explains both postulates of Bohr at once and, in Schrodinger's treatment, gives an impeccable theory of the structure of atoms. De Broglie's assumption received full confirmation by experiment. It turned out that during the passage and reflection of electrons in crystals, sharp diffraction phenomena are revealed. By the arrangement of diffraction rings or bands, one can accurately measure the length of electron waves, and it exactly agrees with formula (5). Thus, indeed, all elementary particles, both material and light, are always accompanied by waves; the duality is not only the nature of light but also of matter. The nature of de Broglie's 'material' waves remains unclear; in any case, these waves are different from electromagnetic light waves. The theory of quanta completely violates the scheme of classical physics. All attempts to explain quanta on the basis of classical mechanics and electrodynamics proved unsuccessful, and it becomes clear that classical physics is only a particular limiting case of true quantum physics, just as geometric optics is a particular limiting case of wave optics. Classical laws should be explained on the basis of the theory of quanta, but not the other way around.