Formulation, Interpretation and Application of non-Commutative Quantum Mechanics

Abstract

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.

11 pages

References in corpus (2)

• Spectrum of the non-commutative spherical well
• On the role of twisted statistics in the noncommutative degenerate electron gas

Cited by in corpus (11)

• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• A unifying perspective on the Moyal and Voros products and their physical meanings
• Minimal areas from q-deformed oscillator algebras
• Semiclassical and quantum description of motion on noncommutative plane
• Spectrum of the three dimensional fuzzy well
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Scattering in three-dimensional fuzzy space
• Bound state energies and phase shifts of a non-commutative well
• Voros product and noncommutative inspired black holes
• An Unfolded Quantization for Twisted Hopf Algebras
• On the noncommutative eikonal