Geodesic
Two-dimensional hydrogen atom. I. Elliptic basis
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 99-117 
L. G. Mardoyan; G. S. Pogosyan; A. N. Sisakyan; V. M. Ter-Antonyan. Two-dimensional hydrogen atom. I. Elliptic basis. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 99-117. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a9/
@article{TMF_1984_61_1_a9,
     author = {L. G. Mardoyan and G. S. Pogosyan and A. N. Sisakyan and V. M. Ter-Antonyan},
     title = {Two-dimensional hydrogen atom. {I.} {Elliptic} basis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {99--117},
     year = {1984},
     volume = {61},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a9/}
}
TY  - JOUR
AU  - L. G. Mardoyan
AU  - G. S. Pogosyan
AU  - A. N. Sisakyan
AU  - V. M. Ter-Antonyan
TI  - Two-dimensional hydrogen atom. I. Elliptic basis
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 99
EP  - 117
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a9/
LA  - ru
ID  - TMF_1984_61_1_a9
ER  - 
%0 Journal Article
%A L. G. Mardoyan
%A G. S. Pogosyan
%A A. N. Sisakyan
%A V. M. Ter-Antonyan
%T Two-dimensional hydrogen atom. I. Elliptic basis
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 99-117
%V 61
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a9/
%G ru
%F TMF_1984_61_1_a9

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

A two-dimensional hydrogen atom is analyzed in elliptic coordinates. Separation of the variables reduces the problem to the solution of the Ince equation in the complex plane subject to certain boundary conditions. It is shown that in the limits $R\rightarrow 0$ and $R\rightarrow\infty$ ($R$ is a parameter that specifies the elliptic coordinates) the obtained solutions go over to polar and parabolic bases, respectively. The explicit form of the elliptic basis is given for the lowest quantum states.

[1] London R., Amer. J. Phys., 27 (1959), 649–655 | DOI

[2] Shibuya T., Wufman C. E., Amer. J. Phys., 33 (1965), 570–574 | DOI | MR

[3] Fock V. A., Z. Phys., 98 (1935), 145–154 | DOI

[4] Eisenhart J. P., Phys. Rev., 74 (1948), 87–89 | DOI | MR | Zbl

[5] Coulson C. A., Robinson P. D., Proc. Phys. Soc., 71 (1958), 815–827 | DOI | Zbl

[6] Komarov I. V., Ponomarev L. I., Slavyanov S. Yu., Sferoidalnye i kulonovskie sferoidalnye funktsii, Nauka, M., 1976 | MR | Zbl

[7] Mardoyan L. G., Pogosyan G. S., Sissakyan A. N., Ter-Antonyan V. M., J. Phys. A, 16 (1983), 711–728 | DOI | MR | Zbl

[8] Arscott F. M., Proc. Roy. Soc. Edinburg, A67 (1967), 265–275 | MR

[9] Zaslow B., Zandler M. E., Amer. Y. Phys., 35 (1967), 1118–1119 | DOI | MR

[10] Mors F. M., Feshbakh G., Metody matematicheskoi fiziki, IL, M., 1958 | MR

[11] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, Nauka, M., 1973 | MR

[12] Cisneros A., McIntosh N. V., J. Math. Phys., 10 (1968), 277–286 | DOI