Numerical implementation of Einstein-Brillouin-Keller quantization for arbitrary potentials

Numerical implementation of Einstein-Brillouin-Keller quantization for arbitrary potentials

The Einstein-Brillouin-Keller (EBK) quantization equation is used to determine the energy levels of a two-body system with an arbitrary central potential that allows for bound states. The treatment is based on the conservation laws and avoids both the Newtonian and Schrödinger differential equations...

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Veröffentlicht in:American journal of physics 2006-07, Vol.74 (7), p.572-577
Hauptverfasser: Larkoski, Andrew J., Ellis, David G., Curtis, Lorenzo J.
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Mathematical functions
Nonlinear equations
Physics
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container_title American journal of physics
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creator Larkoski, Andrew J.
Ellis, David G.
Curtis, Lorenzo J.
description The Einstein-Brillouin-Keller (EBK) quantization equation is used to determine the energy levels of a two-body system with an arbitrary central potential that allows for bound states. The treatment is based on the conservation laws and avoids both the Newtonian and Schrödinger differential equations. Because analytic solutions for the energy levels do not exist in general, the EBK condition is applied using the Newton-Raphson method and the radial probability density is computed. Potentials appropriate for a diatomic molecule are considered and the effect of the angular momentum on the radial distribution, the nature of the classical orbits, and the possibility of closed orbits is studied.
doi_str_mv 10.1119/1.2192788
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subjects Mathematical functions
Nonlinear equations
Physics
title Numerical implementation of Einstein-Brillouin-Keller quantization for arbitrary potentials
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