The time-dependent Schr "odinger equation with piecewise constant\n potentials

2017/09/07 by Natalie E. Sheils, Sheils, Natalie E, Bernard Deconinck +1
Physics and Astronomy · Engineering · #Quantum optics and atomic interactions #Electromagnetic Simulation and Numerical Methods #Terahertz technology and applications

paper · pdf · doi:10.48550/arxiv.1709.02450

Abstract

The linear Schr "odinger equation with piecewise constant potential in one\nspatial dimension is a well-studied textbook problem. It is one of only a few\nsolvable models in quantum mechanics and shares many qualitative features with\nphysically important models. In examples such as "particle in a box" and\ntunneling, attention is restricted to the time-independent Schr "odinger\nequation. This paper combines the Unified Transform Method and recent insights\nfor interface problems to present fully explicit solutions for the\ntime-dependent problem.\n

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