Quasipotential wave functions of a relativistic harmonic oscillator and Pollaczek polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 254-260
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To construct the radial part of the wave function in the
quasipotential model of a relativistic harmonic oscillator,
modified Pollaczek polynomials $\mathscr{P}_n^{\lambda;l}(r)$ with
parameters $\lambda>0$ and $l=0,1,2,\dots$ are introduced. An
orthogonality condition, the generating function, and various
recursion relations are obtained. It is shown that in the limiting
case when $\lambda\rightarrow\infty$ the polynomials
$\mathscr{P}_n^{\lambda;l}(r)$ go over into generalized Laguerre
polynomials.
@article{TMF_1984_58_2_a10,
author = {N. M. Atakishiyev},
title = {Quasipotential wave functions of a relativistic harmonic oscillator and {Pollaczek} polynomials},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {254--260},
publisher = {mathdoc},
volume = {58},
number = {2},
year = {1984},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a10/}
}
TY - JOUR AU - N. M. Atakishiyev TI - Quasipotential wave functions of a relativistic harmonic oscillator and Pollaczek polynomials JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1984 SP - 254 EP - 260 VL - 58 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a10/ LA - ru ID - TMF_1984_58_2_a10 ER -
N. M. Atakishiyev. Quasipotential wave functions of a relativistic harmonic oscillator and Pollaczek polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 2, pp. 254-260. http://geodesic.mathdoc.fr/item/TMF_1984_58_2_a10/