Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems

Article, Preprint English OPEN
Bagchi, B. ; Fring, A. (2009)
  • Publisher: Elsevier
  • Related identifiers: doi: 10.1016/j.physleta.2009.09.054
  • Subject: General Relativity and Quantum Cosmology | QC | High Energy Physics - Theory | Quantum Physics

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.
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