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TMF, 2015, Volume 183, Number 2, Pages 329–336 (Mi tmf8707)  

This article is cited in 3 scientific papers (total in 3 papers)

Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models

Liyan Liu, Qinghai Hao

College of Science, Civil Aviation University of China, Tianjin, China

Abstract: 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

Funding Agency Grant Number
National Natural Science Foundation of China 11247274
11075115
Fundamental Research Funds for the Central Universities 3122014K006


DOI: https://doi.org/10.4213/tmf8707

Full text: PDF file (347 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:2, 730–736

Bibliographic databases:

PACS: 03.65.Db;03.65.Fd; 03.65.Ge
Received: 08.05.2014

Citation: Liyan Liu, Qinghai Hao, “Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models”, TMF, 183:2 (2015), 329–336; Theoret. and Math. Phys., 183:2 (2015), 730–736

Citation in format AMSBIB
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\paper Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models
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\pages 730--736
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. Liu, Ch. Hou, L. Wei, “The quasi-exactly solvable problems for two dimensional quantum systems”, Mosc. Univ. Phys. Bull., 72:1 (2017), 36–38  crossref  isi  scopus
    2. R. Szmytkowski, “Two-dimensional hydrogen-like atom in a weak magnetic field”, Eur. Phys. J. Plus, 133:8 (2018), 311  crossref  isi  scopus
    3. Szmytkowski R., “Relativistic Two-Dimensional Hydrogen-Like Atom in a Weak Magnetic Field”, Ann. Phys., 401 (2019), 174–192  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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