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arXiv · 1709.02450

The time-dependent Schrödinger equation with piecewise constant potentials

Natalie E Sheils·Bernard Deconinck
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Abstract

The linear Schrödinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with physically important models. In examples such as "particle in a box" and tunneling, attention is restricted to the time-independent Schrödinger equation. This paper combines the Unified Transform Method and recent insights for interface problems to present fully explicit solutions for the time-dependent problem.

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Natalie E Sheils, Bernard Deconinck. 2018-06-28. The time-dependent Schrödinger equation with piecewise constant potentials. https://arxiv.org/abs/1709.02450

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