A new classical theory of electrons

1951 ◽  
Vol 209 (1098) ◽  
pp. 291-296 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Classical Theory ◽  
Physical Significance ◽  
Gauge Transformations

In the theory of the electromagnetic field without charges, the potentials are not fixed by the field, but are subject to gauge transformations. The theory thus involves more dynamical variables than are physically needed. It is possible by destroying the gauge transformations to make the superfluous variables acquire a physical significance and describe electric charges. One gets in this way a simplified classical theory of electrons, which appears to be more suitable than the usual one as a basis for a passage to the quantum theory.

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

scholarly journals Free paths and transport phenomena gases and the quantum theory of collisions. I.—The rigid sphere model

1933 ◽  
Vol 141 (844) ◽  
pp. 434-453 ◽  
Keyword(s):  
Quantum Theory ◽  
Classical Theory ◽  
Transport Phenomena ◽  
Wave Theory ◽  
Molecular Beams ◽  
Rigid Sphere ◽  
Sphere Model ◽  
Experimental Proof ◽  
Additional Advantage ◽  
Recent Developments

The necessity for the use of quantum mechanics in the theory of atomic phenomena is most clearly manifest in the study of collision processes. Diffrac­tion effects have been observed in the scattering of electrons from crystals and by atoms, while the recent developments of molecular ray technique have made it possible to establish the existence of cross-grating spectra in the reflection of molecular beams from crystal surfaces. In view of the importance of wave theory in these phenomena, it is clearly necessary to examine the conditions under which the classical theory of gases must be modified and to determine the nature of the modifications. Such an investigation receives added importance owing to the possibility of experimental test by molecular ray methods. Also, considerable interest is attached to the possibility of direct experimental proof of the Bose-Einstein statistics for neutral atoms and molecules from collision experiments as has already been possible for α-particles. In order to develop the quantum theory of collisions in a form suitable for this purpose, we first discuss the simplest model which bears sufficient re­semblance to the actual facts, and so we consider the rigid sphere model for gas atoms. This model has already proved valuable in the classical theory of transport phenomena and has the additional advantage of permitting an exact quantum mechanical solution. It will be seen that the results obtained by the use of this model are of great interest and suggest several new lines of investigation, both experimental and theoretical. Finally, a method for dealing with the general case of any law of force will be discussed.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

The Hydrogen Bond

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Marc Henry
Keyword(s):  
Hydrogen Bond ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Quantum Physics ◽  
Energy Levels ◽  
Strong Association ◽  
Emergent Property ◽  
Water Molecules ◽  
Linear Coupling ◽  
Non Linear

The claim that chemistry has been explained in terms of quantum theory is received wisdom. Yet quantum physics is unable to explain the strong association of water molecules in liquid or ice. Marc Henry suggests the hydrogen bond is an emergent property of matter resulting from a non-linear coupling between quantified energy levels of water molecules and a quantified internal electromagnetic field.

From Classical to Quantum Mechanics

2021 ◽  
pp. 207-219
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Classical Theory ◽  
Constrained Systems ◽  
Experimental Results ◽  
Basic Assumptions ◽  
Original Approach

In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.

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