Exact Solutions for Compactly Supported Parabolic and Landau Barriers
Peter Collas, David Klein
TL;DR
This paper derives exact solutions for the Schrödinger equation with specific potential barriers, providing explicit formulas for transmission, reflection, and dwell times, enhancing understanding of quantum tunneling phenomena.
Contribution
It introduces exact analytical solutions for parabolic and hyperbolic secant potential barriers, including their combinations, with explicit expressions for scattering coefficients and dwell times.
Findings
Exact solutions for parabolic and hyperbolic secant barriers
Explicit formulas for transmission and reflection coefficients
Calculated dwell times for potential barriers
Abstract
We derive exact solutions to the one-dimensional Schr\"odinger equation for compact support parabolic and hyperbolic secant potential barriers, along with combinations of these types of potential barriers. We give the expressions for transmission and reflection coefficients and calculate some dwell times of interest.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum Mechanics and Non-Hermitian Physics · Nonlinear Photonic Systems