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2012

The Constraints and Spectra of a Deformed Quantum Mechanics

Ching, Chee-Leong, Parwani, Rajesh R., Singh, Kuldip

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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.

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