Nonlinear Schrödinger equation and semiclassical description of the microwave-to-optical frequency conversion based on the Lamb–Retherford experiment

Abstract

I show that Lamb-Retherford experiment can be fully described within the framework of classical field theory without using concepts such as the discrete states of the atom and jump-like electron transitions between them. The rate of stimulated decay of the metastable state of a hydrogen atom in an external periodic electric field is determined. The dependence of this rate on the frequency and amplitude of the external electric field, as well as on the parameters of the atom, has been obtained. It is shown that the maximum value of the stimulated decay rate of the metastable state of a hydrogen atom is achieved at an external electric field frequency equal to the frequency shift corresponding to either the fine structure of the hydrogen atom or the Lamb shift.

Nonlinear effects in WDM Networks

“…Now, if we follow the same steps as were done for the Self Phase Modulation, we"ll end up with two equations: One for the field distribution: Fj (x, y) and one for the evolution of the envelope: A j (z)e − jβ 0 jz is a function of distance on the optical fibre. Taking the nonlinear variation of the Schrodinger equation, we"re talking about the Nonlinear Schrodinger (NLS) equation, an equation belonging to classical field theory [16]. This equation has, among others, applications related to the propagation of light in nonlinear optical fibres [17].…”

Nonlinear Pauli Equation

“…Semiclassical theories have made significant progress in describing the basic quantum effects that make up the experimental foundation of modern quantum mechanics, such as the Compton effect [1][2][3][4]18], photoelectric effect [5,21], thermal radiation [22,25], spontaneous emission and spontaneous transitions [6-12, 15-17, 19, 24], light-matter interactions [7,20], induced emission [6,7,20,22], Lamb shift [6,7,9], the Lamb-Retherford experiments [23], etc. It can be argued that at present there is not a single basic quantum effect that has not been described within the semiclassical theory.…”

“…It was shown in [17][18][19][20][21][22][23] that it is possible to construct a completely classical theory that successively and consistently describes and explains all the basic quantum effects within the framework of classical field theory without any quantization or other additional hypotheses. This theory is based on the original idea of Schrödinger [26,27] that the wave functions (scalar, spinor or bispinor) described by the wave equations allows constructing real parameters that can be interpreted as the electric charge density and electric current density, which are continuously distributed in space.…”

“…Equation ( 5), ( 6) is a nonlinear Schrödinger equation, and allows correctly describing the spontaneous emission spectrum of an atom, as well as all the basic quantum effects [18][19][20][21][22][23], which are traditionally described in the framework of QED using the second quantization apparatus [29]. For example, the rearrangement of the structure of the hydrogen atom during spontaneous emission, which in QED is called "spontaneous transition" and is traditionally explained by a zitterbewegung caused by fluctuations of the QED-vacuum, from the point of view of equation ( 5) turns out to be a completely trivial effect that has a simple explanation within the framework of classical electrodynamics [19].…”

“…Despite the success of equation ( 1) (or, what is the same, equation ( 5)) in explaining a number of basic "quantum" regularities [18][19][20][21][22][23], from the point of view of classical electrodynamics, it remains inexplicable why the electrically charged electron field does not "feel" its own electrostatic field, but at the same time "feels" the electrostatic field of other charges and the non-stationary (radiation) component of its own electromagnetic field, which occurs during spontaneous emission.…”