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Title: Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem

Abstract

A model, which admits normalizable wave functions of the Schroedinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell's fish-eye. This is performed with the help of a suitably chosen conformal mapping.

Authors:
 [1]
  1. Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100 Torun (Poland), E-mail: amak@fizyka.umk.pl
Publication Date:
OSTI Identifier:
21336069
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 324; Journal Issue: 12; Other Information: DOI: 10.1016/j.aop.2009.09.012; PII: S0003-4916(09)00187-0; Copyright (c) 2009 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:
97 MATHEMATICAL METHODS AND COMPUTING; CONFORMAL MAPPING; COUPLING CONSTANTS; EXACT SOLUTIONS; INTEGRAL CALCULUS; POTENTIALS; SCHROEDINGER EQUATION; WAVE FUNCTIONS

Citation Formats

Makowski, Adam J. Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem. United States: N. p., 2009. Web. doi:10.1016/j.aop.2009.09.012.
Makowski, Adam J. Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem. United States. doi:10.1016/j.aop.2009.09.012.
Makowski, Adam J. Tue . "Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem". United States. doi:10.1016/j.aop.2009.09.012.
@article{osti_21336069,
title = {Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem},
author = {Makowski, Adam J.},
abstractNote = {A model, which admits normalizable wave functions of the Schroedinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell's fish-eye. This is performed with the help of a suitably chosen conformal mapping.},
doi = {10.1016/j.aop.2009.09.012},
journal = {Annals of Physics (New York)},
number = 12,
volume = 324,
place = {United States},
year = {Tue Dec 15 00:00:00 EST 2009},
month = {Tue Dec 15 00:00:00 EST 2009}
}