Geodesic
Approximate analytic solution of the~Logunov--Tavkhelidze equation for a~one-dimensional oscillator potential in the~ relativistic configuration representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 455-468

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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.
Keywords: quasipotential equation, relativistic configuration representation, integral equation, harmonic oscillator, wave function, energy spectrum, Macdonald function.
Mots-clés : Sturm–Liouville problem 
@article{TMF_2022_211_3_a4,
     author = {Yu. A. Grishechkin and V. N. Kapshai},
     title = {Approximate analytic solution of {the~Logunov--Tavkhelidze} equation for a~one-dimensional oscillator potential in the~ relativistic configuration representation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {455--468},
     publisher = {mathdoc},
     volume = {211},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_3_a4/}
}
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Yu. A. Grishechkin; V. N. Kapshai. Approximate analytic solution of the~Logunov--Tavkhelidze equation for a~one-dimensional oscillator potential in the~ relativistic configuration representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 455-468. http://geodesic.mathdoc.fr/item/TMF_2022_211_3_a4/