Lower bounds for quartic anharmonic and double-well potentials

DOI10.1063/1.530375zbMath0767.35049OpenAlexW2077888556MaRDI QIDQ4697270

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Publication date: 29 June 1993

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

Full work available at URL: https://doi.org/10.1063/1.530375

zbMATH Keywords

Schrödinger equationaccurate lower boundslower eigenvalue spectrum

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (1)

Approximation method for the density matrix of an anharmonic-oscillator gas

Cites Work

• A unified treatment of Schrodinger's equation for anharmonic and double well potentials
• Some observations on the nature of solutions for the interaction V(x)=x²+(λx²/(1+gx²))
• Exact solutions of the Schrödinger equation for nonseparable anharmonic oscillator potentials in two dimensions
• Dynamic-group approach to the x2+λx2/(1+g x2) potential
• The Schrodinger equation for the x²+λx²/(1+gx²) interaction
• A Rodrigues formula approach to determining closed-form solutions to the Schrödinger equation for symmetric anharmonic oscillators
• Exact analytical eigenfunctions for the x²+ λ x²/(1+gx²) interaction
• A Procedure for Estimating Eigenvalues
• Pairs of analytical eigenfunctions for the x²+ λ x²/(1 + gx²) interaction
• On the simultaneous eigenproblem for the x²- λ x²(1 + gx²)^-1interaction: extension of Gallas' results

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