arXiv 1307.78992013-07-30hep-thquant-ph

Harmonic oscillator with minimal length, minimal momentum, and maximal momentum uncertainties in SUSYQM framework

M. Asghari, P. Pedram, K. Nozari

备注：: 14 pages, 1 figure, to appear in Physics Letters B
发表信息：: Phys. Lett. B 725, 451 (2013)
DOI：: 10.1016/j.physletb.2013.07.030

英文摘要：

We consider a Generalized Uncertainty Principle (GUP) framework which predicts a maximal uncertainty in momentum and minimal uncertainties both in position and momentum. We apply supersymmetric quantum mechanics method and the shape invariance condition to obtain the exact harmonic oscillator eigenvalues in this GUP context. We find the supersymmetric partner Hamiltonians and show that the harmonic oscillator belongs to a hierarchy of Hamiltonians with a shift in momentum representation and different masses and frequencies. We also study the effect of a uniform electric field on the harmonic oscillator energy spectrum in this setup.

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