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Title: Constraints and spectra of a deformed quantum mechanics
Authors: Ching, C.-L.
Parwani, R.R. 
Singh, K. 
Issue Date: 31-Oct-2012
Citation: Ching, C.-L., Parwani, R.R., Singh, K. (2012-10-31). Constraints and spectra of a deformed quantum mechanics. Physical Review D - Particles, Fields, Gravitation and Cosmology 86 (8) : -. ScholarBank@NUS Repository.
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 subclass of which also implies 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 semiclassical 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. © 2012 American Physical Society.
Source Title: Physical Review D - Particles, Fields, Gravitation and Cosmology
ISSN: 15507998
DOI: 10.1103/PhysRevD.86.084053
Appears in Collections:Staff Publications

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