Open perturbation and the Riccati equation: Algebraic determination of the quartic anharmonic oscillator energies and eigenfunctions

DOI10.1063/1.532147zbMath0888.34070OpenAlexW2006405547MaRDI QIDQ4378298

G. Bessis, Nik Bessis

Publication date: 11 June 1998

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

Full work available at URL: https://doi.org/10.1063/1.532147

zbMATH Keywords

analytical solutionSchrödinger equationsRiccati equationuse of computer algebra\(gx^ 4\)-anharmonic oscillator equationopen perturbation technique

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (3)

Computing energy eigenvalues of anharmonic oscillators using the double exponential sinc collocation method ⋮ Bound states and ``resonances in quantum anharmonic oscillators ⋮ An extended scenario for the Schrödinger equation

Uses Software

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Cites Work

• Accurate eigenvalues and eigenfunctions of simple quantum-mechanical systems by means of the Riccati-Hill method
• Perturbative solution for the generalised anharmonic oscillators
• Eigenvalues from the Riccati equation
• The quartic oscillator
• A note on the Schrodinger equation for the potential A exp(-x²)-l(l+1)/x²
• Perturbed factorization of the singular anharmonic-oscillator eigenequation
• Lower Bounds for Eigenvalues of Schrödinger's Equation
• The Factorization Method

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