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Schrödinger equation with periodic potentials.

Mugassabi, Souad
Publication Date
2011-05-27
End of Embargo
Supervisor
Vourdas, Apostolos
Keywords
Schrödinger equation, Eigenvectors, Weyl function, Wigner function
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Creative Commons License
The University of Bradford theses are licenced under a Creative Commons Licence.
Peer-Reviewed
Open Access status
Accepted for publication
Institution
University of Bradford
Department
Department of Mathematics
Awarded
2010
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Abstract
The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential, are presented. Wigner and Weyl functions, corresponding to the solutions of Schrödinger equation, are also studied. It is also shown that they are very sensitive to the value of the parameter y.
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http://hdl.handle.net/10454/4895
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Type
Thesis
Qualification name
PhD
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