Effective technique of numerical investigation of systems with complicated geometry of a potential

Abstract

We have developed the technique of a quantum wave impedance determination for the sequence of not only constant potentials but also for potentials of forms for which the solution of a Shrödinger equation exists at least in terms of special functions. The method was applied for a deformed double-barrier system and as a result the dependence of a transmission probability $T$ on an energy $E$ of a particle at different parameters of this system was numerically calculated. Obtained results can be applied to the numerical investigation of a quantum mechanical systems with complicated geometry (spatial structure) of a potential.

arXiv comment11 pages, 3 figures

References in corpus (7)

• The transfer matrix: a geometrical perspective
• Reformulation of a transmission and reflection problems in terms of a quantum wave impedance function
• 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
• Application of a quantum wave impedance method for zero-range singular potentials
• Application of a quantum wave impedance method for study of infinite and semi-infinite periodic media
• Numerical study of quantum mechanical systems using a quantum wave impedance approach

Cited by in corpus (3)

• 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