Exact solution of the Schrödinger equation with a Lennard-Jones potential

Abstract

The Schrödinger equation with a Lennard-Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the connection factors between Floquet and Thomé solutions. The energies of the bound states result as zeros of a function defined by a convergent series whose successive terms are calculated by means of recurrence relations. The procedure gives also the wave functions expressed either as a linear combination of two Laurent expansions, at moderate distances, or as an asymptotic expansion, near the singular points. A table of the critical intensities of the potential, for which a new bound state (of zero energy) appears, is also given.

arXiv commentDedicated to Prof. Albert Bramon (Universitat Autònoma de Barcelona) on occasion of his 70th anniversary. The final publication is available at http://link.springer.com

References in corpus (3)

• Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules
• Spiked oscillators: exact solution
• Scattering length for Lennard-Jones potentials

Cited by in corpus (4)

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• Global solution of the cubic oscillator
• Scattering by infinitely rising one-dimensional potentials
• An Accurate Zeroth-Order Perturbation Theory for Solving Power-Law Potentials within the Framework of the Asymptotic Iteration Method