scientific article; zbMATH DE number 809157

zbMath0835.35120MaRDI QIDQ4852907

T. F. Pankratova

Publication date: 30 November 1995

Full work available at URL: http://www.numdam.org/item?id=AIHPA_1995__62_4_361_0

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zbMATH Keywords

Schrödinger equationanalytic potentialGaussian-like asymptoticsnondegenerated minimum

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with quantum mechanics (35Q40) 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.)
• The Schrödinger equation and canonical perturbation theory
• 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
• On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems
• The Exponential Representation of Canonical Matrices
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