Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 329-336
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We use a simple mathematical method to solve the problem of a two-dimensional hydrogen-like atom in the inhomogeneous magnetic fields $\mathbf B=(k/r)\mathbf z$ and $\mathbf B=(k/r^3)\mathbf z$. We construct a Hamiltonian that takes the same form as the Hamiltonian of a hydrogen-like atom in the homogeneous magnetic fields and obtain the energy spectrum by comparing the Hamiltonians. The results show that the whole spectrum of the atom in the magnetic field $\mathbf B=(k/r)\mathbf z$ can be obtained, and the problem is exactly solvable in this case. We find analytic solutions of the Schrödinger equation for the atom in the magnetic field $\mathbf B=(k/r^3)\mathbf z$ for particular values of the magnetic strength $k$ and thus present a quasi-exactly solvable model.
Keywords:
quasi-exactly solvable system, exactly solvable system.
@article{TMF_2015_183_2_a8,
author = {Liyan Liu and Qinghai Hao},
title = {Planar hydrogen-like atom in inhomogeneous magnetic fields: {Exactly} or quasi-exactly solvable models},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {329--336},
publisher = {mathdoc},
volume = {183},
number = {2},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a8/}
}
TY - JOUR AU - Liyan Liu AU - Qinghai Hao TI - Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 329 EP - 336 VL - 183 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a8/ LA - ru ID - TMF_2015_183_2_a8 ER -
%0 Journal Article %A Liyan Liu %A Qinghai Hao %T Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models %J Teoretičeskaâ i matematičeskaâ fizika %D 2015 %P 329-336 %V 183 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a8/ %G ru %F TMF_2015_183_2_a8
Liyan Liu; Qinghai Hao. Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 329-336. http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a8/