Hermite polynomial ansatz for a multidimensional well

DOI10.1007/BF02355166zbMath0930.35049OpenAlexW2092174824MaRDI QIDQ1807451

T. F. Pankratova

Publication date: 22 November 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/68515

zbMATH Keywords

ray methodanalytic potentialDiophantine conditionnondegenerate minimum

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic expansions of solutions to PDEs (35C20) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Cites Work

• Semiclassical analysis of low lying eigenvalues. II: Tunneling
• Analytic wavefront sets and operators with multiple characteristics
• Germes de configurations legendriennes stables et fonctions d'Airy-Weber généralisées. (Germs of stable Legendre configurations and generalized Airy-Weber functions.)
• Double wells
• New approach to the semiclassical limit of quantum mechanics. I: Multiple tunnelings in one dimension
• Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation \(hu_ t=h^ 2\Delta u/2-V(x)u\)
• Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential
• Modes and quasimodes
• Multiple wells in the semi-classical limit I
• Multiple Wells in the Semi-Classical Limit III - Interaction Through Non-Resonant Wells
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