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 tunnelling, 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 57-83 |
| Number of pages | 27 |
| Journal | European Journal of Applied Mathematics |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 18 2020 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© Cambridge University Press 2018.
Keywords
- Fokas Method
- Schrödinger equation
- Unified Transform Method