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Keywords = anisotropic harmonic oscillator

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11 pages, 549 KB  
Article
Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators
by James Moran and Véronique Hussin
Quantum Rep. 2019, 1(2), 260-270; https://doi.org/10.3390/quantum1020023 - 15 Nov 2019
Cited by 12 | Viewed by 4315
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 [...] Read more.
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. Full article
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