Singular anharmonicities and the analytic continued fractions. II. The potentials V(r)=a r2+b r−4+c r−6

DOI10.1063/1.528867zbMath0711.35104OpenAlexW2032523823MaRDI QIDQ3496658

Miloslav Znojil

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1063/1.528867

zbMATH Keywords

Schrödinger equationMathieu functionsLaurent series solutionssingular anharmonicities

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Convergence and divergence of continued fractions (40A15) Numerical methods for partial differential equations, boundary value problems (65N99)

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Cites Work

• The rotating harmonic oscillator eigenvalue problem. I. Continued fractions and analytic continuation
• Extended continued fractions and energies of the anharmonic oscillators
• Potential r²+λr²/(1+gr²) and the analytic continued fractions
• Elementary bound states for the power-law potentials
• Vectorial continued fractions and an algebraic construction of effective Hamiltonians
• Scattering of Ions by Polarization Forces

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