Extended continued fractions and energies of the anharmonic oscillators

DOI10.1063/1.525841zbMath0532.34018OpenAlexW2033327107MaRDI QIDQ3314178

Miloslav Znojil

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525841

zbMATH Keywords

Green's functionharmonic oscillatorbinding energiesradial Schrödinger equationasymptotic structure of wavefunctionsextended continued fractionregular power-series solution

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Convergence and divergence of continued fractions (40A15) Ordinary differential operators (34L99)

Related Items

The generalized continued fractions and potentials of the Lennard-Jones type ⋮ Exact solutions of the Schrödinger equation for a class of three-dimensional isotropic anharmonic oscillators ⋮ Singular anharmonicities and the analytic continued fractions. II. The potentials V(r)=a r2+b r−4+c r−6 ⋮ On the elementary Schrödinger bound states and their multiplets ⋮ On the power-series construction of bound states. I. The energies as zeros of the infinite Hill determinants ⋮ Bound states and ``resonances in quantum anharmonic oscillators ⋮ On the summation of the Birkhoff–Gustavson normal form of an anharmonic oscillator ⋮ On the power-series construction of Schrödinger bound states. II. The effective Hill determinants

Cites Work

• Analytic solutions of the general anharmonic-oscillator problem
• Elementary bound states for the power-law potentials
• Analytic continued fraction technique for bound and confined states for a class of confinement potentials