Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 52, Number 2 (2000), 269-292.
Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space
The spectra of the quadratic Hamiltonians on the twodimensional Euclidean space are determined completely by using the theory of the metaplectic representation. In some cases, the corresponding heat kernels are studied in connection with the well-definedness of the Wiener integrations. A proof of the Lévy formula for the stochastic area and a relation between the real and complex Hermite polynomials are given in our framework.
J. Math. Soc. Japan, Volume 52, Number 2 (2000), 269-292.
First available in Project Euclid: 10 June 2008
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35P05: General topics in linear spectral theory
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis 60H05: Stochastic integrals
MATSUMOTO, Hiroyuki; UEKI, Naomasa. Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space. J. Math. Soc. Japan 52 (2000), no. 2, 269--292. doi:10.2969/jmsj/05220269. https://projecteuclid.org/euclid.jmsj/1213107373