Time-dependent q-deformed bi-coherent states for generalized uncertainty relations

Abstract

We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the entire deformed Fock space can be constructed explicitly, we define the q-deformed bi-coherent states. We verify the generalized Heisenberg's uncertainty relations projected onto these states. For the initial value in time, the states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time and for the parameter of noncommutativity $\theta =0$, the inequalities are saturated for the simultaneous measurement of the position-momentum observables. When the time evolves the uncertainty products are different from their values at the initial time and do not always respect the generalized uncertainty relations.

17 pages

References in corpus (5)

• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Time-dependent q-deformed coherent states for generalized uncertainty relations
• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Minimal areas from q-deformed oscillator algebras

Cited by in corpus (3)

• A comparative review of four formulations of noncommutative quantum mechanics
• Coherent states for a system of an electron moving on plane
• Coherent states for a system of an electron moving in a plane: case of discrete spectrum