Single point potentials with total resonant tunneling

Abstract

Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar tunneling properties are studied in considerable detail. Particularly, in the zero-range limit when the potentials are squeezed to a single point, sharp peaks with total transmission are observed at certain (positive and negative) quantized values of the potential strength constant forming infinite discrete sets. Beyond these sets, the barrier-well structures behave as a perfectly reflecting wall. The transcendental equations with respect to potential strengths, the solutions of which determine transmission (resonance) sets, are derived. In this regard, both the models are exactly solvable. The energy dependence of an incident particle is shown to reveal a resonance behavior, being completely different from that observed in a typical double barrier structure.

8 figures

References in corpus (6)

• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• Coupling in the singular limit of thin quantum waveguides
• 1D Schrödinger operators with short range interactions: two-scale regularization of distributional potentials
• Potential-controlled filtering in quantum star graphs
• Controlling a resonant transmission across the ${\delta }^{\prime }$-potential: the inverse problem
• Schrödinger operators on star graphs with singularly scaled potentials supported near the vertices

Cited by in corpus (6)

• Distribution theory for Schrödinger's integral equation
• Families of one-point interactions resulting from the squeezing limit of the sum of two- and three-delta-like potentials
• An approximation to the Woods-Saxon potential based on a contact interaction
• Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space
• Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis
• Application of a quantum wave impedance method for zero-range singular potentials