Scattering of a plane electromagnetic wave by free and bound wave packets is analyzed by semiclassical radiation theory. It is shown that the theory gives the correct answer to the question of radiation intensity in the photoelectric effect and to the correlation problem in Compton scattering. The expression for the intensity of the scattered radiation differs from the cross section which is derived from the model based on the particle nature of the electromagnetic field. The meaning of this difference is discussed. Low frequency spectrum of the scattered radiation on a bound charge is obtained.
Scattering of a plane electromagnetic wave by free and bound wave packets is analyzed by semiclassical radiation theory. It is shown that the theory gives the correct answer to the question of radiation intensity in the photoelectric effect and to the correlation problem in Compton scattering. The expression for the intensity of the scattered radiation differs from the cross section which is derived from the model based on the particle nature of the electromagnetic field. The meaning of this difference is discussed. Low frequency spectrum of the scattered radiation on a bound charge is obtained.
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.
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.
Abstract In this work we analyze the wave–particle aspects of radiation in (incoherent) Compton scattering in the radiation energy range from 2–100 keV. From the calculated cross sections of the scattering from the electron (positron), hydrogen and positronium we construct the interpretation functions (IFs), where our assertion is that the Compton scattering from the free electron (positron) is an established example of the particle behavior of radiation. These IFs estimate the possibility of the interpretation of radiation in terms of waves or particles in an analogy with the analysis carried out in the coherent scattering of light. Based on these IFs we propose a new criterion for the estimation of the validity of the impulse approximation (IA).
Many quantum phenomena, traditionally described by quantum electrodynamics, can be calculated within the framework of so-called semiclassical theory, in which atoms are described by the wave equations of quantum mechanics (Schrödinger, Dirac, etc.), while light is described by classical electrodynamics without quantization of the radiation. These phenomena include the photoelectric effect, the Compton effect, the Lamb shift, radiative effects, spontaneous emission, the Hanbury Brown and Twiss effect, etc. In this paper, I show that the double-slit experiment can also be calculated in detail in terms of semiclassical theory if we take into account the discrete (atomic) structure of matter. I show that the results of a semiclassical simulation of the “linear” double-slit experiment coincide with predictions of wave theory only for low-intensity light and for short exposure time, while stricter dependences exist for long-term exposure. The semiclassical theory is used for calculation of the “nonlinear” double-slit experiment with an intense laser beam in which multiphoton and tunnel excitation of atoms on a photographic plate occurs. The Born rule for light is derived from the semiclassical theory.
Chapter I The origins of quantum physics I The Compton effect — a strange dichotomy in the nature of electromagnetic radiation In a series of experiments conducted between 1919 and 1923, Arthur Holly Compton (Figure 1.1) investigated the scattering of monochromatic (single-wavelength) X-rays from graphite targets. He found that the radiation scattered at an angle 0 to the incident beam contained, in addition to radiation of the same wavelength as the incident radiation, a second component with a considerably longer wavelength. The existence of this second component in the scattered radiation could not be explained by the well-established theory of the scattering of electromagnetic waves by electrons. Compton considered instead the process illustrated in Figure 1.2, in which a particle of electromagnetic radiation, collides with a slow moving electron, which then recoils absorbing some of the X-ray particle’s energy. Treating the process as a collision between particles, and using only the (relativistic) conservation laws of energy and momentum, Compton was able to account for the effect completely. However, at the same time, in the same experiment, Compton was using interference effects, depending wholly on the wave model, in order to determine the wavelength of the scattered radiation. So here was an experiment which apparently required the simultaneous use of both the wave and particle models of electromagnetic radiation for the interpretation of the results! The existence of this strange dichotomy in the nature of electromagnetic radiation was just one indication of the need for a radical revision of views regarding the physical world.
A Schrödinger type equation for a mathematical probability amplitude ψ(x,t), is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M, moving in a potential V(x). The particle phase space probability density is denoted W(x,p,t) and the entire system is immersed in the "vacuum" zero-point electromagnetic radiation . We show that the generalized Liouville equation is reduced to a non-quantized Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. Our derivation will be based on a simple Fourier transform of the non-quantized phase space probability distribution W(x,p,t). For convenience, we introduce in this Fourier transform an auxiliary constant α, with dimension of action, and an auxiliary coordinate denoted by y. We shall prove that α is equal to the Planck's constant present in the momentum operator of the Schrödinger equation. Moreover, we shall show that this momentum operator is deeply related with the ubiquitous zero-point electromagnetic radiation. It is also important to say that we do not assume that the mathematical amplitude ψ(x,t) is a de Broglie matter-wave, in other words, the wave-particle duality hypothesis is not used within our work. The implications of our study for the standard interpretation of the photoelectric effect is discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunnelling phenomenon and in the Compton's effect.