The Birkhoff–Gustavson normal form of one-dimensional double-well Hamiltonians

DOI10.1063/1.528350zbMath0685.46048OpenAlexW2028856196MaRDI QIDQ4735647

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Publication date: 1989

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

Full work available at URL: https://doi.org/10.1063/1.528350

zbMATH Keywords

Birkhoff-Gustavson normal formdegree 4semiclassical quantum numbersanalytic continuation of the BGNF seriesclassical perioddouble-well anharmonic oscillators with polynomial potentials ofdouble-well anharmonic oscillators with polynomial potentials of degree 4semiclassical results for all energies

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Miscellaneous applications of functional analysis (46N99)

Related Items (2)

Canonical perturbation expansions to large order from classical hypervirial and Hellmann–Feynman theorems ⋮ Perturbation theory and the classical limit of quantum mechanics

Cites Work

• Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems
• On the integrals of canonical systems
• Anharmonic oscillators and generalized hypergeometric functions
• On the summation of the Birkhoff–Gustavson normal form of an anharmonic oscillator
• Canonical transformations depending on a small parameter
• Perturbation method in the theory of nonlinear oscillations

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