Convergent expansions for tunneling

DOI10.1007/BF01210848zbMath0579.47050OpenAlexW1980719103MaRDI QIDQ1067187

Jean-Michel Combes, Pierre Duclos, Ruedi Seiler

Publication date: 1983

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01210848

zbMATH Keywords

Schrödinger operatoreffects of tunneling in one-dimensional multiple wellmeasure the splitting between eigenvalues

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) General theory of ordinary differential operators (47E05) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)

Related Items (19)

A remark on eigenvalue splittings for one-dimensional double-well Hamiltonians ⋮ Unnamed Item ⋮ The shape resonance ⋮ On the mathematical theory of predissociation ⋮ On the absence of resonances for Schrödinger operators with non- trapping potentials in the classical limit ⋮ PHASE TRANSITIONS AND QUANTUM EFFECTS IN ANHARMONIC CRYSTALS ⋮ A flea on Schrödinger's cat ⋮ Unnamed Item ⋮ Return to Equilibrium, Non-self-adjointness and Symmetries, Recent Results with M. Hitrik and F. Hérau ⋮ Tunneling effect between radial electric wells in a homogeneous magnetic field ⋮ Instantons and splitting ⋮ Unnamed Item ⋮ Spectral stability under tunneling ⋮ Effet tunnel entre puits degeneres ⋮ Spectral geometry: Two exactly solvable models ⋮ Tunneling resonances in systems without a classical trapping ⋮ Unnamed Item ⋮ Structural isomers, double wells, resonances, and Dirichlet decoupling ⋮ Connections and effective S-matrix in triangle representation for quantum scattering

Cites Work

• Krein's formula and one-dimensional multiple-well
• Double wells
• New approach to the semiclassical limit of quantum mechanics. I: Multiple tunnelings in one dimension
• Supersymmetry and Morse theory
• The band-structure of a one-dimensional, periodic system in a scaling limit
• Instantons, double wells and large deviations
• HYPERCONTRACTIVE AND RELATED BOUNDS FOR DOUBLE WELL SCHRÖDINGER HAMILTONIANS
• Unnamed Item
• Unnamed Item

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