The concept of a resonant state is widely invoked in the study of quantum heterostructure devices. It is the means by which the operation of the resonant-tunneling diode is understood[1,2]. Resonant states also participate in the operation of quantum-well photodetectors. There has not, however, been any systematic way to locate and characterize all of the resonant states in a structure of arbitrary complexity.
This paper describes a technique for numerically evaluating the resonant states produced by an arbitrarily complex potential. It employs the Quantum Transmitting Boundary Method (QTBM) of Lent and Kirkner[3] to describe the coupling of the wavefunction to semi-infinite domains on either side of the region of interest.