Noncommutative quantum mechanics

2000/10/31 by J. Gamboa, M. Loewe, J. C. Rojas · 15 citations
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevd.64.067901

published as Phys.Rev. D64 (2001) 067901 · Minors corrections and some references removed. To appear in PRD

arxiv created 2001/06/14 · openalex publication_date 2001/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter \ensuremathθ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(H_HO,L_z), where H_HO is the Hamiltonian of the two-dimensional harmonic oscillator and L_z is the z component of the angular momentum. For other finite values of \ensuremathθ the model can be solved by using perturbation theory.

Citations

• Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)

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