Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators
arXiv:1911.06389 · doi:10.3390/quantum1020023
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 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.
12 pages, 5 figures, International Conference on Squeezed States and Uncertainty Relations, Madrid, Spain, 2019