Coherent states in noncommutative quantum mechanics

Abstract

Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.

References in corpus (4)

• Spectrum of the non-commutative spherical well
• Coherent States of the Deformed Heisenberg-Weyl Algebra in Noncommutative Space
• Structure of Noncommutative Fock space
• Free particle on noncommutative plane -- a coherent state path integral approach

Cited by in corpus (10)

• A comparative review of four formulations of noncommutative quantum mechanics
• "Stringy" Coherent States Inspired By Generalized Uncertainty Principle
• Heat flow and noncommutative quantum mechanics in phase-space
• Noncommutative phase-space effects in thermal diffusion of Gaussian states
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Classical limits of quantum mechanics on a non-commutative configuration space
• Coherent States on Hilbert Modules
• Dirac equation with a magnetic field in 3D non-commutative phase space
• Time Dependent Variational Principle and Coherent State Orbits for a Trapped Ion
• Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories