The Heisenberg Oscillator
  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. 
Veronique Fischer
math.AP math.RT math.SP