2009•arXiv (Cornell University)Open access

Displacement and Squeeze Operators of a Three-Dimensional Harmonic Oscillator and Their Associated Quantum States

Mehdi Miri, Sina Khorasani

Abstract

We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated the Wigner function for the three-dimensional harmonic oscillator and from the analysis of time evolution of this function, the quantum Liouville equation is also presented. Further properties of the quantum states including Mandel's Q and quadrature squeezing parameters are discussed as well.

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Key concepts: Harmonic oscillator, Creation and annihilation operators, Coherent states, Quantum harmonic oscillator, Displacement (psychology), Squeezed coherent state, Quadrature (astronomy), Quantum