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Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems

Bagchi, B. and Fring, A. (2009). Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems. Physics Letters A, 373(47), pp. 4307-4310. doi: 10.1016/j.physleta.2009.09.054

Abstract

Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems may be treated in a similar framework as quasi/pseudo and/or PT-symmetric systems, which have recently attracted much attention. For a newly proposed deformation of exponential type we compute the minimal uncertainty and minimal length, which are essential in almost all approaches to quantum gravity.

Publication Type: Article
Publisher Keywords: OPERATORS, SYMMETRY
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/692
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