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arXiv:2001.07652 · Springer eBooks

A New Method for Constructing Squeezed States for the Isotropic 2D Harmonic Oscillator

James Moran, Véronique Hussin

Published Aug 8, 2020• 1 citation
arXivHTMLPDF
DOI
10.1007/978-3-030-55777-5_24

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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 S U ( 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.