Two-dimensional hydrogen atom. I. Elliptic basis
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 99-117
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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.
@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},
publisher = {mathdoc},
volume = {61},
number = {1},
year = {1984},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a9/ %G ru %F TMF_1984_61_1_a9
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/