Exact Solutions for Compactly Supported Parabolic and Landau Barriers
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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.
💡 Research Summary
The paper presents a comprehensive analytical treatment of one‑dimensional quantum tunneling through two families of smooth, compact‑support potentials: (i) a symmetric parabolic barrier that is non‑zero only on the interval (
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