### Abstract

The authors have employed algebraic methods to calculate the bound-state spectra of a non-relativistic hydrogen atom subjected to a wide class of perturbations. Their procedure exploits the linearity of the complete (perturbed) Hamiltonian in the generators of the SO(2, 2) Lie algebra which follows naturally from the separation of variables in Schrodinger's equation in parabolic coordinates. Appropriate transformations then allow the Hamiltonian to be expressed as a linear combination of the compact generators of the two underlying SO(2, 1) algebras. They give some examples for which the bound-state spectra can be obtained completely analytically.

Original language | English |
---|---|

Article number | 012 |

Pages (from-to) | 803-809 |

Number of pages | 7 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 22 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Dec 1989 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*22*(7), 803-809. [012]. https://doi.org/10.1088/0305-4470/22/7/012

**The perturbed hydrogen atom : Some new algebraic results.** / Kais, S.; Cohen, M.; Levine, R. D.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 22, no. 7, 012, pp. 803-809. https://doi.org/10.1088/0305-4470/22/7/012

}

TY - JOUR

T1 - The perturbed hydrogen atom

T2 - Some new algebraic results

AU - Kais, S.

AU - Cohen, M.

AU - Levine, R. D.

PY - 1989/12/1

Y1 - 1989/12/1

N2 - The authors have employed algebraic methods to calculate the bound-state spectra of a non-relativistic hydrogen atom subjected to a wide class of perturbations. Their procedure exploits the linearity of the complete (perturbed) Hamiltonian in the generators of the SO(2, 2) Lie algebra which follows naturally from the separation of variables in Schrodinger's equation in parabolic coordinates. Appropriate transformations then allow the Hamiltonian to be expressed as a linear combination of the compact generators of the two underlying SO(2, 1) algebras. They give some examples for which the bound-state spectra can be obtained completely analytically.

AB - The authors have employed algebraic methods to calculate the bound-state spectra of a non-relativistic hydrogen atom subjected to a wide class of perturbations. Their procedure exploits the linearity of the complete (perturbed) Hamiltonian in the generators of the SO(2, 2) Lie algebra which follows naturally from the separation of variables in Schrodinger's equation in parabolic coordinates. Appropriate transformations then allow the Hamiltonian to be expressed as a linear combination of the compact generators of the two underlying SO(2, 1) algebras. They give some examples for which the bound-state spectra can be obtained completely analytically.

UR - http://www.scopus.com/inward/record.url?scp=36149034814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149034814&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/22/7/012

DO - 10.1088/0305-4470/22/7/012

M3 - Article

VL - 22

SP - 803

EP - 809

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

M1 - 012

ER -