Solution of the Logunov–Tavkhelidze Equation for the Three-Dimensional Oscillator Potential in the Relativistic Configuration Representation

Abstract

Approximate analytical and numerical solutions of the three-dimensional Logunov–Tavkhelidze equation are found for the spherically symmetric case. Solutions are obtained in momentum and relativistic configuration representations. The wave functions in the relativistic configuration representation have additional zeroes compared to the wave functions of the nonrelativistic harmonic oscillator in the coordinate representation.