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

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

2009-12-17

arxiv.org/abs/0912.3335v3

International Journal of Optics and Photonics, vol. 4, no. 1, pp. 9-22 (2010)

Physics

Quantum Physics

Accepted for publication in the International Journal of Optics and Photonics

Scientific paper

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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