Anharmonic oscillator: Constructing the strong coupling expansions

DOI10.1063/1.528187zbMath0694.35201OpenAlexW2058680826MaRDI QIDQ3469618

A. G. Ushveridze, Alexander~V. Turbiner

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528187

zbMATH Keywords

Schrödinger equationstrong coupling expansionanharmonic oscillatornonlinearization techniqueintegral perturbation theoryrapidly convergent perturbation series

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Perturbation theories for operators and differential equations in quantum theory (81Q15) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (15)

Convergence radii for eigenvalues of tri-diagonal matrices ⋮ Quasi-exactly solvable cases of an \(N\)-dimensional symmetric decatic anharmonic oscillator. ⋮ Construction of \(\mathcal {PT}\)-asymmetric non-hermitian Hamiltonians with CPT symmetry ⋮ Convergent series for lattice models with polynomial interactions ⋮ r D oscillators with arbitrary D>0 and perturbation expansions with Sturmians ⋮ Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions ⋮ Bound states and ``resonances in quantum anharmonic oscillators ⋮ The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations ⋮ Convergent series for polynomial lattice models with complex actions ⋮ A high-precision study of anharmonic-oscillator spectra ⋮ Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. II. Quartic and sextic anharmonicity cases ⋮ Infinite lattice models by an expansion with a non-Gaussian initial approximation ⋮ Radial anharmonic oscillator: Perturbation theory, new semiclassical expansion, approximating eigenfunctions. I. Generalities, cubic anharmonicity case ⋮ Anharmonic oscillator: a solution ⋮ Computer algebra and large scale perturbation theory

Cites Work

• Analytical expressions for the eigenvalues of anharmonic oscillators
• Divergence of Perturbation Theory in Quantum Electrodynamics
• Perturbation Theory for the One-Dimensional Wave Equation

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