2015/04/30 by Laure Gouba · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.4927263
published as J. Math. Phys. 56, 073507(2015) · 17 pages
arxiv created 2015/07/28 · arxiv updated 2015/07/29
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 θ=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.