Geodesic
Relativistic linear oscillator under the action of a constant
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 481-494

Voir la notice de l'article provenant de la source Math-Net.Ru

An exactly solvable relativistic model of a linear oscillator is considered in detail in the presence of a constant external force in both the momentum representation and the relativistic configuration representation. It is found that in contrast to the nonrelativistic case, depending on the magnitude of the force, both discrete and continuous energy spectra are possible. It is shown that in the case of a discrete spectrum, the wave functions in the momentum representation are expressed in terms of the Laguerre polynomials, and in the relativistic configuration representation, in terms of the Meixner–Pollaczek polynomials. Integral and differential–difference formulas are found connecting the Laguerre and Meixner–Pollaczek polynomials. A dynamical symmetry group is constructed.
Keywords: relativistic linear oscillator model, uniform field, finite-difference equation, dynamical symmetry group, relation between orthogonal polynomials. 
@article{TMF_2021_208_3_a7,
     author = {Sh. M. Nagiyev and R. M. Mir-Kassimov},
     title = {Relativistic linear oscillator under the action of a constant},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {481--494},
     publisher = {mathdoc},
     volume = {208},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a7/}
}
TY  - JOUR
AU  - Sh. M. Nagiyev
AU  - R. M. Mir-Kassimov
TI  - Relativistic linear oscillator under the action of a constant
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 481
EP  - 494
VL  - 208
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a7/
LA  - ru
ID  - TMF_2021_208_3_a7
ER  - 
%0 Journal Article
%A Sh. M. Nagiyev
%A R. M. Mir-Kassimov
%T Relativistic linear oscillator under the action of a constant
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 481-494
%V 208
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a7/
%G ru
%F TMF_2021_208_3_a7
Sh. M. Nagiyev; R. M. Mir-Kassimov. Relativistic linear oscillator under the action of a constant. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 481-494. http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a7/