Connection between Coulomb and harmonic oscillator potentials in relativistic quantum mechanics

Details Connection between Coulomb and harmonic oscillator potentials in relativistic quantum mechanics Connection between Coulomb and harmonic oscillator potentials in relativistic quantum mechanics

2008-09-26

arxiv.org/abs/0809.4528v4

Physics

Quantum Physics

8 pages

Scientific paper

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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