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## Schrödinger equation with periodic potentials.

### Abstract

The Schrödinger equation ... is considered. The solution of this equation\ud is reduced to the problem of finding the eigenvectors of an infinite matrix.\ud The infinite matrix is truncated to a finite matrix. The approximation due\ud to the truncation is carefully studied. The band structure of the eigenvalues\ud is shown. The eigenvectors of the multiwells potential are presented. The\ud solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that\ud the energy is slightly greater than the maximum value of the potential, are\ud presented. Wigner and Weyl functions, corresponding to the solutions of\ud Schrödinger equation, are also studied. It is also shown that they are very\ud sensitive to the value of the parameter y.Garyounis University and Libyan Cultural Affair

Topics: Schrödinger equation, Eigenvectors, Weyl function, Wigner function
Publisher: Department of Mathematics
Year: 2010