Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators

Abstract

In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the $SU(2)$ coherent states, where these are then used as the basis of expansion for Schrödinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.

arXiv comment12 pages, 5 figures, International Conference on Squeezed States and Uncertainty Relations, Madrid, Spain, 2019

References in corpus (2)

• Coherent States for the Hydrogen Atom
• Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator

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• A new method for constructing squeezed states for the isotropic 2D harmonic oscillator
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