%0 Journal Article
%T The Heisenberg oscillator
%A V¨¦ronique Fischer
%J Bulletin of Mathematical Sciences
%@ 1664-3615
%D 2012
%I Springer
%R 10.1007/s13373-012-0021-z
%X In this short note, we determine the spectrum of the Heisenberg oscillator which is the operator defined as $L+|x|^2+|y|^2$ on the Heisenberg group $H_1=\mathbb{ R} ^2_{x,y}\times \mathbb{ R} $ where L stands for the positive sublaplacian.
%K Nilpotent Lie groups
%K Harmonic oscillator
%K Representation of nilpotent Lie groups
%U http://link.springer.com/article/10.1007/s13373-012-0021-z