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arXiv · 1204.1642

The Constraints and Spectra of a Deformed Quantum Mechanics

Chee-Leong Ching·Rajesh R. Parwani·Kuldip Singh
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Abstract

We examine a deformed quantum mechanics in which the commutator between coordinates and momenta is a function of momenta. The Jacobi identity constraint on a two-parameter class of such modified commutation relations (MCR's) shows that they encode an intrinsic maximum momentum; a sub-class of which also imply a minimum position uncertainty. Maximum momentum causes the bound state spectrum of the one-dimensional harmonic oscillator to terminate at finite energy, whereby classical characteristics are observed for the studied cases. We then use a semi-classical analysis to discuss general concave potentials in one dimension and isotropic power-law potentials in higher dimensions. Among other conclusions, we find that in a subset of the studied MCR's, the leading order energy shifts of bound states are of opposite sign compared to those obtained using string-theory motivated MCR's, and thus these two cases are more easily distinguishable in potential experiments.

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Chee-Leong Ching, Rajesh R. Parwani, Kuldip Singh. 2012-04-07. The Constraints and Spectra of a Deformed Quantum Mechanics. https://doi.org/10.1103/physrevd.86.084053

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