Geodesic
Potentials that admit solution of the one-dimensional time-independent Schrödinger equation in terms of known functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 59-65 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that thereexist only two five-parameter potentials that admit solution of the Schrödinger equation in hypergeometric functions. An analysis establishes the connection between these potentials and ones known in the literature. 
@article{TMF_1991_88_1_a8,
     author = {A. M. Goncharenko and V. A. Karpenko and V. N. Mogilevich},
     title = {Potentials that admit solution of the one-dimensional time-independent {Schr\"odinger} equation in terms of known functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {59--65},
     year = {1991},
     volume = {88},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a8/}
}
TY  - JOUR
AU  - A. M. Goncharenko
AU  - V. A. Karpenko
AU  - V. N. Mogilevich
TI  - Potentials that admit solution of the one-dimensional time-independent Schrödinger equation in terms of known functions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 59
EP  - 65
VL  - 88
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a8/
LA  - ru
ID  - TMF_1991_88_1_a8
ER  - 
%0 Journal Article
%A A. M. Goncharenko
%A V. A. Karpenko
%A V. N. Mogilevich
%T Potentials that admit solution of the one-dimensional time-independent Schrödinger equation in terms of known functions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 59-65
%V 88
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a8/
%G ru
%F TMF_1991_88_1_a8
A. M. Goncharenko; V. A. Karpenko; V. N. Mogilevich. Potentials that admit solution of the one-dimensional time-independent Schrödinger equation in terms of known functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/TMF_1991_88_1_a8/

[1] Brekhovskikh L. M., Volny v sloistykh sredakh, Nauka, M., 1973 | MR

[2] Infeld L., Hull T. E., Rev. Mod. Phys., 23:1 (1951), 21–68 | DOI | MR | Zbl

[3] Flyugge Z., Zadachi po kvantovoi mekhanike, T. I, Mir, M., 1974 | MR

[4] Natanzon G. A., Vestn. LGU, 1971, no. 10, 21–28 | MR

[5] Natanzon G. A., TMF, 38:2 (1979), 219–229 | MR | Zbl

[6] Mors F. M., Feshbakh G., Metody teoreticheskoi fiziki, IL, M., 1958 | MR

[7] Rosen N., Morze P. M., Phys. Rev., 42 (1932), 210 | DOI

[8] Manning M. F., Rosen N., Phys. Rev., 44 (1933), 953

[9] Bose A. K., Nuovo Cim., 32:3 (1964), 679 | DOI | MR | Zbl

[10] Goncharenko A. M., Karpenko V. A., Mogilevich V. N., Izv. AN BSSR, ser. fiz.- mat. nauk, 1979, no. 3, 90

[11] Nikiforov A. F., Uvarov V. B., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1978 | MR

[12] Mogilevich V. N., Izv. AN BSSR, ser. fiz.-mat. nauk, 1981, no. 2, 121