Minimal length uncertainty relation and the hydrogen atom. (English) Zbl 0991.81047

Brau, F.

J. Phys. A, Math. Gen. 32, No. 44, 7691-7696 (1999).

Summary: We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on an energy spectrum. We use this method to calculate the harmonic oscillator spectrum and find that the corrections are in agreement with a previous calculation. Then, we apply this approach to obtain the hydrogen atom spectrum and we find that splittings of degenerate energy levels appear. Comparison with experimental data yields an interesting upper bound for the deformation parameter of the Heisenberg algebra.

MSC:

81R50	Quantum groups and related algebraic methods applied to problems in quantum theory
81S05	Commutation relations and statistics as related to quantum mechanics (general)
81V45	Atomic physics
81Q15	Perturbation theories for operators and differential equations in quantum theory

Keywords:

deformed Heisenberg algebra; energy spectrum; harmonic oscillator spectrum; hydrogen atom spectrum