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Media type:
E-Article
Title:
General series solution for finite square-well energy levels for use in wave-packet studies
Contributor:
Aronstein, David L.;
Stroud, C. R.
Published:
American Association of Physics Teachers (AAPT), 2000
Published in:
American Journal of Physics, 68 (2000) 10, Seite 943-949
Language:
English
DOI:
10.1119/1.1285868
ISSN:
1943-2909;
0002-9505
Origination:
Footnote:
Description:
We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum (which target a particular energy range of the potential well for high accuracy), for global approximations of the energy spectrum (which provide analytic expressions of reasonable accuracy for the entire range of bound states), and for numerical methods. This solution also provides an analytic description of dynamical phenomena; with it, we compute the time scales of classical motion, revivals, and super-revivals for wave-packet states excited in the well.