P. Enders, CAN THE TRANSMISSION-LINE MATRIX-METHOD YIELD STATIONARY SOLUTIONS OFTHE TIME-DEPENDENT SCHRODINGER-EQUATION, International journal of numerical modelling, 9(4), 1996, pp. 321-323
By virtue of the success of the transmission line matrix method (TLM)
in solving heat and matter diffusion problems, it should also be appli
cable to the time-dependent Schrodinger equation. The occurrence of co
mplex-valued circuit elements does not destroy the unconditional stabi
lity of the routine. But it seems to be impossible to obtain stationar
y (eigen)solutions to this equation as well as separable solutions to
the diffusion equation. It is suggested that this is due to the non-di
ssipativity of the TLM routine.