On the power-series construction of bound states. I. The energies as zeros of the infinite Hill determinants

DOI10.1063/1.528190zbMath0666.34066OpenAlexW2063257873MaRDI QIDQ3818640

Miloslav Znojil

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528190

zbMATH Keywords

bound statespotentialsHill-determinantpower-series construction

Mathematics Subject Classification ID

Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Function-theoretic methods (including power series methods and semicontinuous methods) for summability (40C15)

Related Items (4)

Spiked oscillators: exact solution ⋮ The generalized continued fractions and potentials of the Lennard-Jones type ⋮ On the elementary Schrödinger bound states and their multiplets ⋮ On the power-series construction of Schrödinger bound states. II. The effective Hill determinants

Cites Work

• Analytic continued fraction theory for a class of confinement potentials
• Analytic solutions of the general anharmonic-oscillator problem
• The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation
• Continued fractions and the potential models of confinement-reply to a comment
• Extended continued fractions and energies of the anharmonic oscillators
• The Hill determinant method in application to the sextic oscillator: limitations and improvement

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