Russian Physics Journal

, Volume 61, Issue 9, pp 1645–1652 | Cite as

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

  • Yu. A. GrishechkinEmail author
  • V. N. Kapshai

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.


quasipotential equation harmonic oscillator relativistic configuration representation momentum representation Sturm–Liouville problem integral equation MacDonald function hypergeometric series energy spectrum wave function 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Francisk Skorina Gomel State UniversityGomelBelarus

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