The Heisenberg Oscillator

Details The Heisenberg Oscillator The Heisenberg Oscillator

2011-08-16

arxiv.org/abs/1108.3275v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

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.

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