skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Exactly solvable associated Lame potentials and supersymmetric transformations

Abstract

A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are used to generate new exactly solvable potentials; some of them exhibit an interesting property of periodicity defects.

Authors:
 [1];  [2]
  1. Departamento de Fisica, Cinvestav, AP 14-740, 07000 Mexico DF (Mexico). E-mail: david@fis.cinvestav.mx
  2. City College (C.C.C.B.A.), University of Calcutta, 13 Surya Sen Street, Kolkata 700 012 (India) and Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain). E-mail: gangulyasish@rediffmail.com
Publication Date:
OSTI Identifier:
20976758
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 5; Other Information: DOI: 10.1016/j.aop.2006.07.011; PII: S0003-4916(06)00180-1; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; EXACT SOLUTIONS; FACTORIZATION; PERIODICITY; POTENTIALS; QUANTUM MECHANICS; SUPERSYMMETRY; TRANSFORMATIONS

Citation Formats

Fernandez, David J., and Ganguly, Asish. Exactly solvable associated Lame potentials and supersymmetric transformations. United States: N. p., 2007. Web. doi:10.1016/j.aop.2006.07.011.
Fernandez, David J., & Ganguly, Asish. Exactly solvable associated Lame potentials and supersymmetric transformations. United States. doi:10.1016/j.aop.2006.07.011.
Fernandez, David J., and Ganguly, Asish. Tue . "Exactly solvable associated Lame potentials and supersymmetric transformations". United States. doi:10.1016/j.aop.2006.07.011.
@article{osti_20976758,
title = {Exactly solvable associated Lame potentials and supersymmetric transformations},
author = {Fernandez, David J. and Ganguly, Asish},
abstractNote = {A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are used to generate new exactly solvable potentials; some of them exhibit an interesting property of periodicity defects.},
doi = {10.1016/j.aop.2006.07.011},
journal = {Annals of Physics (New York)},
number = 5,
volume = 322,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • The general solution of the stationary Schroedinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seed solutions for factorization energies inside the gaps.
  • A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0{sup +}) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from {supmore » 58}Ni to {sup 68}Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.« less
  • The three-dimensional Schroedinger equation with an effective mass is solved for a new class of angular momentum dependent potentials with varying depths and shapes. The energy eigenvalues and resonances are given in algebraic form as a function of the effective mass and depth and shape of the potential. The eigenfunctions, scattering function, and Green's function are given in closed form in terms of known special functions. The charge density of /sup 208/Pb is calculated using eigenfunctions of a potential and this charge density is compared to the measured charge density.