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

arXiv:hep-th/0212309

On Parasupersymmetries in Relativistic Coulomb Problem for the Modified Stueckelberg Equation

Artur Sergyeyev

Published Dec 26, 2002• 0 citations
arXivHTMLPDF

Abstract

This paper presents a first example of parasupersymmetric relativistic quantum-mechanical model with non-oscillator-like interaction: the Coulomb problem for the modified Stueckelberg equation, describing a relativistic massive spin-1 particle in the electromagnetic field of a point charge.
DOI
10.48550/arxiv.hep-th/0212309

Related papers

A model with two quantum particles similar to the hydrogen atom

Ruslan Abdulovich Sharipov

The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.

arXiv:1308.0221•Aug 1, 2013•0 citations

On parasupersymmetric Hamiltonians and vector mesons in magnetic fields

N. Debergh

A new Sakata-Taketani equation describing vector mesons in interaction with a constant magnetic field is proposed. It leads to real energies as opposed to relativistic equations, which have already been pointed out, associated with this particular interacting context. In particular, the connection between this new proposal and a specific model coming from parasupersymmetric quantum mechanics is studied.

Journal of Physics A Mathematical and General•Apr 7, 1994•7 citations

Spinor equations in relativistic quantum mechanics

Egon Marx

A set of two first-order equations for classical spinor fields are used to formulate the relativistic quantum mechanics (RQM) of a single massive spin-1/2 particle. These equations are generalized Weyl equations and they are not equivalent to the Dirac equation. They lead to a conserved charge that is not positive definite, thus allowing for a probabilistic interpretation of the wave function in RQM. The charge is also conserved when the fields interact with a scalar field through the charge-current densities.

Journal of Mathematical Physics•Jun 1, 1992•4 citations

Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Vagram M. Mekhitarian

Relativistic invariant equations are proposed for the action function and the wave function based on the invariance of the representation of the generalized momentum. The equations have solutions for any values of the interaction constant of a particle with a field, for example, in the problem of a hydrogen-like atom, when the atomic number of the nucleus Z > 137. Based on the parametric representation of the action, the expression for the canonical Lagrangian, the equations of motion and the expression for the force acting on the charge during motion in an external electromagnetic field are derived. The Dirac equation with the correct inclusion of the interaction for a particle in an external field is presented. In this form, the solutions of the equations are not limited by the value of the interaction constant. The solutions of the problem of charge motion in a constant electric field, problems for a particle in a potential well, and penetration of a particle through a potential barrier, as well as problem of a hydrogen atom are presented.

Journal of Contemporary Physics (Armenian Academy of Sciences)•Jan 1, 2018•5 citations

The new wave equations of relativistic and non-relativistic quantum mechanics

Xiang-Yao Wu, Guo, Yiqing, Xin-Guo Yin

In this work, we give the wave equations of relativistic and non-relativistic quantum mechanics which are different from the Schrödinger and Klein-Gordon equation, and we also give the new relativistic wave equation of a charged particle in an electromagnetic field

arXiv:quant-ph/0312012•Dec 1, 2003•0 citations

Dirac’s new relativistic wave equation in interaction with an electromagnetic field

Narasimhaiengar Mukunda, C. C. Chiang, E. C. G. Sudarshan

Abstract Dirac had discovered a relativistic wave equation for a spinless massive particle with only positive energies. It has a defect: it became inconsistent when electromagnetic interaction was included. In this paper this problem is surmounted simply.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jan 8, 1982•4 citations
The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.
A set of two first-order equations for classical spinor fields are used to formulate the relativistic quantum mechanics (RQM) of a single massive spin-1/2 particle. These equations are generalized Weyl equations and they are not equivalent to the Dirac equation. They lead to a conserved charge that is not positive definite, thus allowing for a probabilistic interpretation of the wave function in RQM. The charge is also conserved when the fields interact with a scalar field through the charge-current densities.
Relativistic invariant equations are proposed for the action function and the wave function based on the invariance of the representation of the generalized momentum. The equations have solutions for any values of the interaction constant of a particle with a field, for example, in the problem of a hydrogen-like atom, when the atomic number of the nucleus Z > 137. Based on the parametric representation of the action, the expression for the canonical Lagrangian, the equations of motion and the expression for the force acting on the charge during motion in an external electromagnetic field are derived. The Dirac equation with the correct inclusion of the interaction for a particle in an external field is presented. In this form, the solutions of the equations are not limited by the value of the interaction constant. The solutions of the problem of charge motion in a constant electric field, problems for a particle in a potential well, and penetration of a particle through a potential barrier, as well as problem of a hydrogen atom are presented.