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ENERGY SPECTRUM OF A q-DEFORMED HYDROGEN ATOM

YANG QING-ZHU, Xu Bo-wei, (1)上海交通大学物理系; (2)上海师范大学物理系

The SOq(4) quantum algebra is used for the description of a q-deformed 3-dimensional hydrogen atom. The energy spectrum and degenercy of the q-deformed 3-dimension and 2-dimensional hydrogen atom are obtained respectively.

Acta Physica SinicaJan 1, 19941 citation

On the q-analogue of the hydrogen atom

M. Kibler, Tidjani Négadi

The discrete spectrum of a q-analogue of the hydrogen atom is obtained from a deformation of the Pauli equations. As an alternative, the spectrum is derived from a deformation of the four-dimensional oscillator arising in the application of the Kustaanheimo-Stiefel transformation to the hydrogen atom. A model of the 2s-2p Dirac shift is proposed in the context of q-deformations.

arXiv:quant-ph/0408151Journal of Physics A Mathematical and GeneralNov 21, 199150 citations

Two models of a q-deformed hydrogen atom

Jonas Gora

Two possible methods of deformation of a hydrogen-like system in terms of the q-(deformed) boson operators are constructed. In the first case the system has SU q (2)(X)SU q (2) symmetry, while in the second S((X) 4 i=1 U q (1)) symmetry. The energy level degeneracy and splitting for both cases are explicitly calculated.

Journal of Physics A Mathematical and GeneralDec 7, 19926 citations

Energy Spectrum of a Two-Parameter Deformed Hydrogen Atom

Zhao-Xian Yu, Ye-Hou Liu

International Journal of Theoretical PhysicsDec 1, 19981 citation

Aq-analogue of a two-dimensional hydrogen atom

Gao-Jian Zeng, Ming Li

International Journal of Theoretical PhysicsJun 1, 19972 citations

The “accidental” degeneracy of the hydrogen atom is no accident

Pranawa C. Deshmukh, Aarthi Ganesan, N. Shanthi +3 more

The Schrödinger equation does not account for the 2n2 degeneracy of the hydrogen atom, which it dismisses as an “accidental” degeneracy. The factor of “2” in the 2n2 degeneracy is well-accounted-for in the relativistic formulation by the two spin states of the electron. The n2 degeneracy is nevertheless not quite an “accident”; it is due to the SO(4), rather than SO(3), symmetry of the hydrogen atom. This result is well known, but is inadequately commented upon in most courses in quantum mechanics and atomic physics, leaving the student wondering about the origins of the n2 degeneracy of the hydrogen atom. A pedagogical analysis of this interesting aspect, which highlights the fundamental principles of quantum mechanics, is presented in this article. While doing so, not only is the n2 degeneracy of the hydrogen atom explained, but its energy spectrum and eigenfunctions are obtained without even using the Schrödinger equation, employing only the fundamental principles of quantum mechanics rather than the Schrödinger equation.The Schrödinger equation does not account for the 2n2 degeneracy of the hydrogen atom, which it dismisses as an “accidental” degeneracy. The factor of “2” in the 2n2 degeneracy is well-accounted-for in the relativistic formulation by the two spin states of the electron. The n2 degeneracy is nevertheless not quite an “accident”; it is due to the SO(4), rather than SO(3), symmetry of the hydrogen atom. This result is well known, but is inadequately commented upon in most courses in quantum mechanics and atomic physics, leaving the student wondering about the origins of the n2 degeneracy of the hydrogen atom. A pedagogical analysis of this interesting aspect, which highlights the fundamental principles of quantum mechanics, is presented in this article. While doing so, not only is the n2 degeneracy of the hydrogen atom explained, but its energy spectrum and eigenfunctions are obtained without even using the Schrödinger equation, employing only the fundamental principles of quantum mechanics rather than the Schrödinger equation.

Canadian Journal of PhysicsAug 28, 20145 citations

Energy spectrum of a q-analogue of the hydrogen atom

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Energy spectrum of a q-analogue of the hydrogen atom

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