Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space

DOI10.2969/jmsj/05220269zbMath0965.35101OpenAlexW2089509314MaRDI QIDQ1574800

Hiroyuki Matsumoto, Naomasa Ueki

Publication date: 12 March 2001

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/05220269

zbMATH Keywords

spectrumHermite polynomialsheat kernelsLévy formulaWiener integrations

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Stochastic integrals (60H05)

Related Items (3)

Eigenvalues and eigenfunctions for the two dimensional Schrödinger operator with strong magnetic field ⋮ Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one ⋮ Markov semi-groups associated with the complex unimodular group \(\mathrm{Sl}(2,{\mathbb{C}})\)

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