The Heisenberg Oscillator

Abstract

In this short note, we determine the spectrum of the Heisenberg oscillator which is the operator defined as $L+|z{|}^2$ on the 3-dimensional Heisenberg group $H_1=\mathbb{C}\times \mathbb{R}$ where $L$ stands for the positive sublaplacian and $z$ for the complex variable of a point of the group.

arXiv comment9 pages; published in Bulletin of Mathematical Sciences, 2012

Cited by in corpus (1)

• Harmonic and Anharmonic Oscillators on the Heisenberg Group