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Semiclassical quantization rules near separatrices

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Publication:1338882
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DOI10.1007/BF02099426zbMath0812.58096MaRDI QIDQ1338882

Pavel M. Bleher

Publication date: 23 November 1994

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


zbMATH Keywords

one-dimensional Schrödinger operatorsemiclassical quantization


Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Geometry and quantization, symplectic methods (81S10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Geometric quantization (53D50)


Related Items

Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae ⋮ Long time evolution of quantum averages near stationary points ⋮ Quantum states of the Kapitza pendulum ⋮ Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems



Cites Work

  • Unnamed Item
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  • Quantum effects near a barrier maximum
  • Extension of the WKB Equation
  • Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders
  • Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
  • The Asymptotic Forms of the Hermite and Weber Functions
  • A WKB-Type Approximation to the Schrödinger Equation
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