AN EIGENVALUE METHOD FOR OPEN-BOUNDARY QUANTUM TRANSMISSION PROBLEMS

We present a numerical technique for open-boundary quantum transmissio n problems which yields, as the direct solutions of appropriate eigenv alue problems, the energies of (i) quasi-bound states and transmission poles, (ii) transmission ones, and (iii) transmission zeros. The eige nvalue problem results from reducing the inhomogeneous transmission pr oblem to a homogeneous problem by forcing the in-coming source term to zero. This homogeneous problem can be transformed to a standard linea r eigenvalue problem. By treating either the transmission amplitude t( E) or the reflection amplitude r(E) as the known source term, this met hod also can be used to calculate the positions of transmission zeros and ones. We demonstrate the utility of this technique with several ex amples, such as single- and double-barrier resonant tunneling and quan tum waveguide systems, including t-stubs and loops. (C) 1995 American Institute of Physics.