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Iterative projection methods for computing relevant energy states of a quantum dot. (English) Zbl 1102.81040

Summary: A computational technique for computing relevant energy levels and corresponding wave functions of an electron confined by a 3D quantum dot embedded in a semiconductor matrix are studied. Assuming an energy and position dependent electron effective mass approximation this problem is governed by a rational eigenvalue problem. We discuss the application of iterative projection method of Arnoldi and Jacobi-Davidson type. Projected problems of small dimension are solved efficiently by safeguarded iteration.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
82D20 Statistical mechanics of solids

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References:

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