English

The Heisenberg Oscillator

Analysis of PDEs 2012-06-15 v2 Representation Theory Spectral Theory

Abstract

In this short note, we determine the spectrum of the Heisenberg oscillator which is the operator defined as L+z2L + |z|^2 on the 3-dimensional Heisenberg group H1=C×RH_1=\mathbb C \times \mathbb R where LL stands for the positive sublaplacian and zz for the complex variable of a point of the group.

Cite

@article{arxiv.1108.3275,
  title  = {The Heisenberg Oscillator},
  author = {Veronique Fischer},
  journal= {arXiv preprint arXiv:1108.3275},
  year   = {2012}
}

Comments

9 pages; published in Bulletin of Mathematical Sciences, 2012

R2 v1 2026-06-21T18:51:10.123Z