The generalized continued fractions and potentials of the Lennard-Jones type

DOI10.1063/1.528644zbMath0708.47035OpenAlexW2008627496MaRDI QIDQ3490520

Miloslav Znojil

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1063/1.528644

zbMATH Keywords

Schrödinger differential equationMathieu functionsgeneralized continued fractionspotentials of the Lennard-Jones typesuperpositions of separate power-law components

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General theory of partial differential operators (47F05) Equations and inequalities involving linear operators, with vector unknowns (47A50) Applications of functional analysis in quantum physics (46N50)

Related Items (4)

Relativistic bound states of spinless particle by the Cornell potential model in external fields ⋮ Dirac equation under scalar, vector, and tensor Cornell interactions ⋮ An analytic estimate of the number of bound states in the Lennard-Jones potentials ⋮ PROTON STATIC PROPERTIES BY USING HYPERCENTRAL CONSTITUENT QUARK MODEL AND ISOSPIN

Cites Work

• Extended continued fractions and energies of the anharmonic oscillators
• Singular anharmonicities and the analytic continued fractions. II. The potentials V(r)=a r2+b r−4+c r−6
• Elementary bound states for the power-law potentials
• The anharmonic oscillator problem: a new algebraic solution
• The Hill determinant method in application to the sextic oscillator: limitations and improvement
• On the power-series construction of bound states. I. The energies as zeros of the infinite Hill determinants
• Scattering of Ions by Polarization Forces

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