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Exact Solutions for Compactly Supported Parabolic and Landau Barriers
Peter Collas, David Klein·January 10, 2026
Quantum PhysicsMathematical Physics
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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.