The time-dependent Schr\"odinger equation with piecewise constant potentials
Analysis of PDEs
2018-07-02 v2
Abstract
The linear Schr\"odinger 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 Schr\"odinger equation. This paper combines the Unified Transform Method and recent insights for interface problems to present fully explicit solutions for the time-dependent problem.
Cite
@article{arxiv.1709.02450,
title = {The time-dependent Schr\"odinger equation with piecewise constant potentials},
author = {Natalie E Sheils and Bernard Deconinck},
journal= {arXiv preprint arXiv:1709.02450},
year = {2018}
}
Comments
30 pages, 12 figures