Abstract
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.
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Acknowledgments
The author is very grateful to Professors Fulvio Ricci and Ari Laptev for insightful discussions.
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Communicated by A. Laptev.
The author thanks the London Mathematical Society and King’s College London for support.
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Fischer, V. The Heisenberg oscillator. Bull. Math. Sci. 2, 181–191 (2012). https://doi.org/10.1007/s13373-012-0021-z
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DOI: https://doi.org/10.1007/s13373-012-0021-z