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

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 $\delta -{\delta }^{\prime }$ 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.

arXiv comment17 pages

References in corpus (11)

• Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide
• Many-body system with a four-parameter family of point interactions in one dimension
• Single point potentials with total resonant tunneling
• Reformulation of a transmission and reflection problems in terms of a quantum wave impedance function
• Directed Polymers with Constrained Winding Angle
• An application of a quantum wave impedance approach for solving a nonsymmetric single well problem
• Quantum wave impedance calculation for an arbitrary piesewise constant potential
• Time dependent delta-prime interactions in dimension one
• An artificial boundary approach for short-ranged interactions
• A perturbative method for resolving contact interactions in quantum mechanics
• Effective field theory for one-dimensional nonrelativistic particles with contact interaction

Cited by in corpus (6)

• Application of a quantum wave impedance method for study of infinite and semi-infinite periodic media
• Effective technique of numerical investigation of systems with complicated geometry of a potential
• Numerical study of quantum mechanical systems using a quantum wave impedance approach
• Analytical representation of an iterative formula for a quantum wave impedance determination in a case of a piecewise constant potential
• An application of a quantum wave impedance method to finite periodic structures
• Application of a quantum wave impedance approach for a quantum capacitance calculation