Transfer Matrix in 1D Schrödinger Problems with Constant and Position‐Dependent Mass

The transfer matrix method is considered for obtaining properties of standard wells and barriers in one‐dimensional Schrödinger problems with constant and position‐dependent mass. The formulae for the energy levels of a well and the transmission coefficient of a barrier are given. The continuity is demonstrated between virtual bound states in a well of position‐dependent mass and the relation between the zero energy gap states of a periodic potential problem with the corresponding energies of the non‐periodic one's with transmission coefficient equal to one. The calculations are carried out for a wide class of potentials profiles.