Canonical perturbation expansions to large order from classical hypervirial and Hellmann–Feynman theorems

DOI10.1063/1.529521zbMath0765.70013OpenAlexW2081399640MaRDI QIDQ4031011

Edward R. Vrscay, S. M. McRae

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1063/1.529521

zbMATH Keywords

energies of perturbed periodic orbitsone-dimensional anharmonic oscillatorsquantum mechanical Rayleigh-Schrödinger perturbation seriesradial Kepler problemsseparable classical Hamiltonians

Mathematics Subject Classification ID

Two-body problems (70F05) Perturbation theories for operators and differential equations in quantum theory (81Q15) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (4)

Application of the quantum mechanical hyperviral theorems to even-power series potentials ⋮ Renormalized perturbation series and the semiclassical limit of quantum mechanics ⋮ Perturbation theory and the classical limit of quantum mechanics ⋮ Algebraic and numerical manipulation of the even-power-series central potentials by means of the hypervirial theorems technique

Cites Work

• The Schrödinger equation and canonical perturbation theory
• Perturbation theory of odd anharmonic oscillators
• Some Applications of Hypervirial Theorems to the Calculation of Average Values
• The algebraic quantisation of the Birkhoff-Gustavson normal form
• Continued fractions and Rayleigh–Schrödinger perturbation theory at large order
• Birkhoff-Gustavson normal form in classical and quantum mechanics
• Nonlinear ‘‘self-interaction’’ Hamiltonians of the form H (0)+λ〈r p〉 r q and their Rayleigh–Schrödinger perturbation expansions
• Semi-classical mechanics in phase space: A study of Wigner’s function
• Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators
• Quantum mechanics as classical mechanics plus quantum corrections: the cubic anharmonic oscillator
• The Birkhoff–Gustavson normal form of one-dimensional double-well Hamiltonians
• Forces in Molecules

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