A new proof for the convergent iterative solution of the degenerate quantum double-well potential and its generalization.

DOI10.1016/S0003-4916(03)00141-6zbMath1037.81042OpenAlexW2063256298MaRDI QIDQ1415327

D. Massart

Publication date: 3 December 2003

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

Full work available at URL: https://doi.org/10.1016/s0003-4916(03)00141-6

zbMATH Keywords

quartic potentialhierarchy theorem

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (6)

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators ⋮ Convergent iterative solutions of Schrödinger equation for a generalized double well potential ⋮ A new approach to solve the low-lying states of the Schrödinger equation ⋮ New ways to solve the Schrödinger equation ⋮ Quasilinearization method and WKB ⋮ Convergent iterative solutions for a Sombrero-shaped potential in any space dimension and arbitrary angular momentum

Cites Work

• Instanton--anti-instanton interaction and asymptotics of the perturbation theory expansion for the double well oscillator
• A new method to derive low-lying \(N\)-dimensional quantum wave functions by quadratures along a single trajectory
• A convergent iterative solution of the quantum double-well potential

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