The time-dependent Schrödinger equation with piecewise constant potentials

Natalie E. Sheils, Bernard Deconinck

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)57-83
Number of pages27
JournalEuropean Journal of Applied Mathematics
Issue number1
StatePublished - Feb 18 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Cambridge University Press 2018.


  • Fokas Method
  • Schrödinger equation
  • Unified Transform Method


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