Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 427-433
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We construct a complex transformation $S_{1\mathbb C}\to S_1$ generalizing the known Hurwitz transformation in the Euclidean space for one-dimensional quantum mechanics. As in the case of the flat space, this transformation allows establishing the connection between the Coulomb problem and the oscillator problem with the Calogero–Sutherland potential added. We fully describe the motion in a Coulomb field in $S_1$ and determine the energy spectrum and the wave functions with the correct normalizing constant.
Keywords:
one-dimensional hydrogen atom, Schrödinger equation, Hurwitz transformation, constant-curvature space.
@article{TMF_2003_135_3_a5,
author = {L. G. Mardoyan and G. S. Pogosyan and G. S. Pogosyan and A. N. Sisakyan},
title = {Coulomb {Problem} in a {One-Dimensional} {Space} with {Constant} {Positive} {Curvature}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {427--433},
publisher = {mathdoc},
volume = {135},
number = {3},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a5/}
}
TY - JOUR AU - L. G. Mardoyan AU - G. S. Pogosyan AU - G. S. Pogosyan AU - A. N. Sisakyan TI - Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2003 SP - 427 EP - 433 VL - 135 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a5/ LA - ru ID - TMF_2003_135_3_a5 ER -
%0 Journal Article %A L. G. Mardoyan %A G. S. Pogosyan %A G. S. Pogosyan %A A. N. Sisakyan %T Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature %J Teoretičeskaâ i matematičeskaâ fizika %D 2003 %P 427-433 %V 135 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a5/ %G ru %F TMF_2003_135_3_a5
L. G. Mardoyan; G. S. Pogosyan; G. S. Pogosyan; A. N. Sisakyan. Coulomb Problem in a One-Dimensional Space with Constant Positive Curvature. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 3, pp. 427-433. http://geodesic.mathdoc.fr/item/TMF_2003_135_3_a5/