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Link between the Relativistic Canonical Quantum Mechanics and the Dirac Equation

В. М. Симулик, I.Yu. Krivsky

The foundations of the relativistic canonical quantum mechanics of a fermionic doublet on the basis of the Schrodinger–Foldy equation of motion are formulated. A brief review of the different ways of the Dirac equation derivation is given. The Dirac equation is derived from the Schrodinger–Foldy equation of the relativistic canonical quantum mechanics. It is shown that our model does not need applying of the negative mass concept of the antiparticle.

Universal Journal of Physics and ApplicationFeb 1, 20148 citations

On the non-relativistic motion equations in the hamiltonian form

В. И. Фущич, A. G. Nikitin, V. A. Salogub

Reports on Mathematical PhysicsApr 1, 19786 citations

A Note on Relativistic Quantum Mechanics

Hartland S. Snyder

Physical ReviewMar 1, 19480 citations

Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching

Olavo Leopoldino da Silva Filho, Marcello Caio Ramon e Barros Ferreira

In this paper, we present a derivation of the relativistic equations of Quantum Mechanics. We focus on the second order equations (both Klein Gordon’s and Dirac’s), since the linear Dirac equation can be derived from these. This derivation is an extension of the same method applied to the non-relativistic case in a in a previous series of articles by us. We show that, to extend the theoretical framework to the relativistic case, we have only to extend the axioms in a relativistically compatible way, as should be the case with any extension of an axiomatic method. We also show that this quantization method throws light in a different way to interpret some descriptors of the usual formalism, mainly those regarding the expression for the probability density function. This, on the other hand, gives the teacher following this approach in classes on the subject to assess the epistemological issue of the role of manuals in the learning of Quantum Mechanics.In this paper, we present a derivation of the relativistic equations of Quantum Mechanics. We focus on the second order equations (both Klein Gordon’s and Dirac’s), since the linear Dirac equation can be derived from these. This derivation is an extension of the same method applied to the non-relativistic case in a in a previous series of articles by us. We show that, to extend the theoretical framework to the relativistic case, we have only to extend the axioms in a relativistically compatible way, as should be the case with any extension of an axiomatic method. We also show that this quantization method throws light in a different way to interpret some descriptors of the usual formalism, mainly those regarding the expression for the probability density function. This, on the other hand, gives the teacher following this approach in classes on the subject to assess the epistemological issue of the role of manuals in the learning of Quantum Mechanics.

Revista Brasileira de Ensino de FísicaJan 1, 20251 citation

Quantum-Mechanical Description of the Fermionic Doublet and Its Link with the Dirac Equation

В. М. Симулик, I.Yu. Krivsky

A brief review of the diﬀerent ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet on the basis of the Schr¨odinger–Foldy equation of motion are formulated. In our approach, the Dirac equation is derived from the Schr¨ odinger–Foldy equation.

Ukrainian Journal of PhysicsDec 1, 201311 citations

Derivation of relativistic quantum mechanics

B. Roy Frieden

Cambridge University Press eBooksDec 10, 19980 citations

Brief Note on Derivation of Equation of Motion in Relativistic Quantum Mechanics

Abstract

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Brief Note on Derivation of Equation of Motion in Relativistic Quantum Mechanics

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