AN EFFICIENT METHOD FOR THE NUMERICAL EVALUATION OF RESONANT STATES

An efficient technique is presented for numerically evaluating the resonant states of semiconductor heterostructures with an arbitrarily complex potential. It employs the modified quantum transmitting boundary method to couple the boundary conditions into the construction of a non-Hermitian discrete Hamiltonian matrix. The resonances are the complex-valued eigenvalues of the corresponding matrix. The boundary terms are energy dependent; therefore the eigenvalue problem is nonlinear. The eigenvalues are located by using a combination of partial-shift tridiagonal LR algorithm for the initial evaluation of eigenvalues and Newton iteration for refinement of the eigenvalues. For one-dimensional problems, this technique is efficient and fast enough to be used in an interactive mode, and it has been incorporated into a general-purpose interactive heterostructure modeling program.