Exact Solutions for Compactly Supported Parabolic and Landau Barriers

2026/01/10 by Peter Collas, David Klein · 1 voice
Physics and Astronomy · #quant-ph #math-ph

paper · pdf

arxiv published 2026/01/10 · arxiv updated 2026/01/28

Abstract

We derive exact solutions to the one-dimensional Schrödinger 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.

Citations

• Tuning the Quasi-bound States of Double-barrier Structures: Insights from Resonant Tunneling Spectra
• Quantum Josephson junction circuits and the dawn of artificial atoms
• Exact solution to the Schrodinger's equation with pseudo-Gaussian potential
• Quantum tunneling and evolution speed in an exactly solvable coupled double-well system
• Tunneling through a parabolic barrier viewed from Wigner phase space
• Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox
• Dissipative quantum systems with a potential barrier: General theory and the parabolic barrier

Discussions

• こういうのってまだ解かれてなかったんだ Exact Solutions for Compact Support Parabolic and Landau Barriers https://arxiv.org/abs/2601.06369 [bsky, 1 points, 0 comments]