Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the  relativistic configuration representation

Yu. A. Grishechkin   ; V. N. Kapshai

Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 455-468

Résumé

We construct approximate analytic solutions of the Logunov–Tavkhelidze equation in the case of a potential that, in the one-dimensional relativistic configuration representation, has the form analogous to the potential of the nonrelativistic harmonic oscillator in the coordinate representation. The wave functions are obtained in both the momentum and relativistic configuration representations. The approximate values of the energy of the relativistic harmonic oscillator are the roots of transcendental equations. The wave functions in the relativistic configuration representation have additional zeros in comparison with the wave functions of the corresponding states of the nonrelativistic harmonic oscillator in the coordinate representation.

Détail

Keywords: quasipotential equation, relativistic configuration representation, integral equation, harmonic oscillator, wave function, energy spectrum, Macdonald function.
Mots-clés : Sturm–Liouville problem

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