AN IMPLICIT SPECTRAL FORMULA FOR GENERALIZED LINEAR SCHRÖDINGER EQUATIONS-Reference-Cited by-同舟云学术

AN IMPLICIT SPECTRAL FORMULA FOR GENERALIZED LINEAR SCHRÖDINGER EQUATIONS

Published:2009-10 Issue:09 Volume:18 Page:1831-1844
ISSN:0218-3013
Container-title:International Journal of Modern Physics E
language:en
Short-container-title:Int. J. Mod. Phys. E

Author:

SCHULZE-HALBERG AXEL¹,GARCÍA-RAVELO JESÚS²,GIL JOSÉ JUAN PEÑA³

Affiliation:

1. Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, USA

2. Escuela Superior de Física y Matemáticas, IPN, Unidad Profesional Adolfo López Mateos, Zacatenco, Edificio 9, 07738 México D.F., México

3. Universidad Autónoma Metropolitana – Azcapotzalco, CBI – Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México D.F., México

Abstract

We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schrödinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schrödinger equation or the Schrödinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Nuclear and High Energy Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218301309013890

Reference16 articles.

1. Sufficient Conditions for an Attractive Potential to Possess Bound States

2. Singular Potentials

3. EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

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