Application of a quantum wave impedance method for zero-range singular potentials

TL;DR

This paper introduces a quantum wave impedance method to analyze quantum systems with zero-range singular potentials, enabling solutions for scattering and bound states in complex potential configurations.

Contribution

It formalizes a quantum wave impedance approach to solve systems with various combinations of delta and piecewise constant potentials, advancing analytical techniques in quantum mechanics.

Findings

Solved scattering and bound states for delta and delta-prime potentials

Developed a formalism for arbitrary combinations of piecewise and delta potentials

Demonstrated the method's applicability to complex quantum systems

Abstract

An application of a quantum wave impedance method for a study of quantum-mechanical systems which con\-tain singular zero-range potentials is considered. It was shown how to reformulate the problem of an investigation of mentioned systems in terms of a quantum wave impedance. As a result both the scattering and bound states problems are solved for systems of single $\delta$, double $\delta$ and single $\delta-\delta'$ potentials. The formalization of solving systems with an arbitrary combination of a piesewise constant potential and a $\delta$-potentials with the help of a quantum wave impedance approach is described.