An eigenvalue method for open-boundary quantum transmission problems

We present a numerical technique for open-boundary quantum transmission problems which yields, as the direct solutions of appropriate eigenvalue problems, the energies of (i) quasi-bound states and transmission poles, (ii) transmission ones, and (iii) transmission zeros. The eigenvalue problem results from reducing the inhomogeneous transmission problem to a homogeneous problem by forcing the in-coming source term to zero. This homogeneous problem can be transformed to a standard linear eigenvalue problem. By treating either the transmission amplitude t(E) or the reflection amplitude r(E) as the known source term, this method also can be used to calculate the positions of transmission zeros and ones. We demonstrate the utility of this technique with several examples, such as single- and double-barrier resonant tunneling and quantum waveguide systems, including t-stubs and loops.