Connection between Coulomb and harmonic oscillator potentials in relativistic quantum mechanics
Bo Fu, Fu-Lin Zhang, Jing-Ling Chen
TL;DR
This paper explores how the Levi-Civita transformation links Coulomb and harmonic oscillator potentials in relativistic quantum mechanics, enabling solutions of Coulomb problems through harmonic oscillator results.
Contribution
It introduces a method using the Levi-Civita transformation to connect Coulomb and harmonic oscillator problems in relativistic equations, providing a new approach to solve Coulomb problems.
Findings
Established a transformation linking Coulomb and harmonic oscillator potentials in relativistic systems.
Provided a method to solve Coulomb problems using harmonic oscillator solutions.
Enhanced understanding of potential connections in relativistic quantum mechanics.
Abstract
The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita transformation. These connections lead to an approach to solve the Coulomb problems using the results of the harmonic oscillator potential in the above-mentioned relativistic systems.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Cold Atom Physics and Bose-Einstein Condensates · Quantum chaos and dynamical systems