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American Journal of Physics -- June 2007 -- Volume 75, Issue 6, pp. 524

Critical dipoles in one, two, and three dimensions

Kevin Connolly and David J. Griffiths

Department of Physics, Reed College, Portland, Oregon 97202

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The Schrödinger equation for a point charge in the field of a stationary electric dipole admits bound states only when the dipole moment exceeds a certain critical value. It is not hard to see why this might be the case, but it is surprisingly difficult to calculate the critical dipole moment. The analogous problem should be simpler in one and two dimensions, but a general theorem forbids critical moments in one dimension, and explicit calculation shows that there is no critical moment in two dimensions.

© 2007 American Association of Physics Teachers

KEYWORDS and PACS

Keywords

Schrodinger equation, bound states, electric moments, physics education

PACS

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History
Received Nov 2006
Accepted Jan 2007
Online May 2007

PUBLICATION DATA

ISSN:

0002-9505 (print)  

Publisher:

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Permalink
http://dx.doi.org/10.1119/1.2710485

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