Journal of Physical Studies 9(4), 304–315 (2005)
DOI: https://doi.org/10.30970/jps.09.304

THE TWO-CENTRE COULOMB PROBLEM IN QUANTUM MECHANICS. AN INFLUENCE OF THE DIMENSIONS

D. I. Bondar^{1}, V. Yu. Lazur^{1}, I. M. Shvab^{1}, S. Chalupka^{2}
¹ Department of Theoretical Physics, Uzhgorod National University,
Voloshin Str. 54, 88 000 Uzhgorod, Ukraine
e-mail: dbondar@univ.uzhgorod.ua
e-mail: lazur@univ.uzhgorod.ua
shvabi@univ.uzhgorod.ua
² Institute of Physics, P.J. \v Safárik University, Jesenná 5,
041 54 Ko\v sice, Slovak Republic

This work investigates the two-centre Coulomb problem. The analysis is carried out in the context of the dimensional influence ($D\geq 3$). Asymptotic solutions of the Schr\" odinger equation with two Coulomb potentials are obtained in the hyperspheroidal coordinate system. These solutions are expressed in the form of confluent Heun functions, particular cases being the Coulomb spheroidal functions. The asymptotic expression for energy for a large intercentre separation of the considered system are obtained and basic properties of the mentioned expressions are studied.

PACS number(s): 02.60.Lj, 02.30.Mv, 02.30.Gp, 03.65.Ge