Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal de physique

Sur l'interprétation de la mécanique quantique. V. Spin et relativité

A.B. Datzeff

Published Jan 1, 1962• 0 citations
Publisher

Abstract

The results of the present work are a summary of those obtained in the previous publications [1]-[4]. In (A) is considered a corpuscule with spin introduced according to the hypothesis of Uhlenbeck and Goudsmit. The probability equations obtained here coincide with the wellknown equations of Pauli. In (B) is found a probability equation for a corpuscule without spin in a relativistic case. It proves that it coincides with the well-known equation of Klein-Gordon. In (C) is studied the movement of a corpuscule with spin in a relativistic case. The probability equations obtained here coincide with the well-known equations of Dirac. The matrices of Pauli as well as those of Dirac are found here to be a conséquence of the probability equations. The results obtained here lead to the conclusion that the interpretation of quantum mechanics developed in the previous works may be spread over the cases, considered here.

DOI
10.1051/jphysrad:01962002304024100

Related papers

THE INTERPRETATION OF QUANTUM MECHANICS. RELATIVISTIC CASE OF A BODY WITH SPIN

A.B. Datzeff

The quantum problem of a body with spin, in the case of relativistic velocities, is treated with the aid of wellknown Dirac equations containing four wave functions. In the present work it is shown that the development of the ideas expressed previously (Compt. rend., 250: 67(1960) and Compt. rend., 254: 434(1962)) leads to the mathematical appliance of the Dirac theory, that is, the interpretation of quantum mechanics given can be transported to Dirac equations. (J.S.R.)

Compt. rend.•Jan 22, 1962•0 citations

Relativistic Quantum Mechanics

Arjun Sharma

The chapter covers some of the essential aspects of relativistic quantum mechanics. The Klein-Gordon equation and its solution in coulombic fields, how to interpret probability density and probability current derived from the Klein-Gordon equation, derivation of the Dirac equation and its covariant form, probability density and probability current for Dirac equation, positive and negative energy eigenvalues in the case of a free particle, constants of motion for relativistic treatment, presence of spin magnetic moment and spin-orbit interaction energy in the Dirac equation, and the solution of the Dirac equation for central potentials and for the hydrogen atom are presented with elegant mathematical treatment and physical interpretations. A modern and reader friendly approach is adopted for derivation of the Dirac equation, constants of motion, and for the solution of the Dirac equation for central potentials. Solved examples and unsolved exercises relating to fundamental concepts of relativistic quantum mechanics are added towards the end of chapter.

CRC Press eBooks•Jun 18, 2021•1 citation

Sur l'interprétation de la mécanique quantique. III. Formalisme mathématique

A.B. Datzeff

En généralisant les idées développées dans les publications [1], [2], on est arrivé ici au formalisme mathématique de la mécanique quantique non relativiste. On a montré que les relations d'incertitude, ainsi que les expériences mentales qui sont liées à leur interprétation, ont toujours un sens statistique et que l'on ne peut pas en tirer de conséquences sur la conduite d'un corpuscule unique.

Journal de physique•Jan 1, 1961•3 citations

Quantum Mechanics Needs No Interpretation

Lubomír Skála, V. Kapsa

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, probability density current, commutation and uncertainty relations, momentum operator, rules for including scalar and vector potentials and antiparticles can be derived from the definition of the mean values of powers of space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrödinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the theory. The limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many-particle systems are also discussed.

arXiv:quant-ph/0412175•Collection of Czechoslovak Chemical Communications•Jan 1, 2005•9 citations

Relativistic Quantum Mechanics

Owen L. de Lange, R. E. Raab

Abstract In this chapter we give a brief introduction to the relativistic equations for spin 0 and spin ½ particles (the Klein-Gordon and Dirac equations), and we solve these equations for two simple problems. Throughout we consider only single-particle theory: thus we do not discuss ‘second quantization’ of the relativistic equations (i.e. the use of quantized fields that create and annihilate particles and antiparticles).

•Nov 28, 1991•3 citations

Stochastic Theory of Quantum Mechanics for Particles with Spin

L. de la Peña-Auerbach

The stochastic theory of quantum mechanics is further developed to include the problem of extended rigid particles, thus allowing the introduction of spin. It is demonstrated that the stochastic equations for the system's center of mass give rise to a generalized Schrödinger equation for integral or half-integral spin; in the particular case of spin ½, upon elimination of the internal variables, Pauli's equation is obtained. A formal simplified relativistic extension of the theory is worked out and shown to lead to Dirac's equation in the case of spin ½ and for a gyromagnetic ratio equal to 2; in the case of arbitrary spin, the theory gives an equation of the Feynman-Gell-Mann type.

Journal of Mathematical Physics•Mar 1, 1971•31 citations
The results of the present work are a summary of those obtained in the previous publications [1]-[4]. In (A) is considered a corpuscule with spin introduced according to the hypothesis of Uhlenbeck and Goudsmit. The probability equations obtained here coincide with the wellknown equations of Pauli. In (B) is found a probability equation for a corpuscule without spin in a relativistic case. It proves that it coincides with the well-known equation of Klein-Gordon. In (C) is studied the movement of a corpuscule with spin in a relativistic case. The probability equations obtained here coincide with the well-known equations of Dirac. The matrices of Pauli as well as those of Dirac are found here to be a conséquence of the probability equations. The results obtained here lead to the conclusion that the interpretation of quantum mechanics developed in the previous works may be spread over the cases, considered here.
The chapter covers some of the essential aspects of relativistic quantum mechanics. The Klein-Gordon equation and its solution in coulombic fields, how to interpret probability density and probability current derived from the Klein-Gordon equation, derivation of the Dirac equation and its covariant form, probability density and probability current for Dirac equation, positive and negative energy eigenvalues in the case of a free particle, constants of motion for relativistic treatment, presence of spin magnetic moment and spin-orbit interaction energy in the Dirac equation, and the solution of the Dirac equation for central potentials and for the hydrogen atom are presented with elegant mathematical treatment and physical interpretations. A modern and reader friendly approach is adopted for derivation of the Dirac equation, constants of motion, and for the solution of the Dirac equation for central potentials. Solved examples and unsolved exercises relating to fundamental concepts of relativistic quantum mechanics are added towards the end of chapter.
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, probability density current, commutation and uncertainty relations, momentum operator, rules for including scalar and vector potentials and antiparticles can be derived from the definition of the mean values of powers of space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrödinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the theory. The limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many-particle systems are also discussed.
The stochastic theory of quantum mechanics is further developed to include the problem of extended rigid particles, thus allowing the introduction of spin. It is demonstrated that the stochastic equations for the system's center of mass give rise to a generalized Schrödinger equation for integral or half-integral spin; in the particular case of spin ½, upon elimination of the internal variables, Pauli's equation is obtained. A formal simplified relativistic extension of the theory is worked out and shown to lead to Dirac's equation in the case of spin ½ and for a gyromagnetic ratio equal to 2; in the case of arbitrary spin, the theory gives an equation of the Feynman-Gell-Mann type.