On the Weyl symbol of the resolvent of the harmonic oscillator. (English) Zbl 1391.35117
In this article, the Weyl symbol of the resolvent of the quantum harmonic oscillator is computed. The quantum harmonic oscillator is given by \(H=-\Delta+x^2\) with \(\Delta\) the Laplacian and \(x^2=\sum_{i=1}^dx_i^2\). Additionally, the properties of the Weyl symbol are studied as well as particular precise bounds on the derivatives which is possible due to the fact that it can be explicitely described.
Reviewer: Andreas Kleefeld (Jülich)
MSC:
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 33C15 | Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\) |
| 47A10 | Spectrum, resolvent |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
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