New Numerical Matrix Methods of Solving the Quasi-One-Dimensional Effective-Mass Equation
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New efficient numerical methods of computing eigenvalues and eigenvectors of quasi-one-dimensional effective-mass Hamiltonian with arbitrary coordinate dependence of charge carrier mass are presented. Within the proposed approach the effective-mass equation is replaced by a nonsymmetric or symmetric matrix eigenproblem which can be analysed numerically with the help of existing computer routines. The presented methods are verified in special semiconductor heterostructure cases that are solvable within other approaches. A generalization of the presented methods for nonparabolic materials is also discussed.
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