Solving the time-dependent Schrödinger equation via Laplace transform
- Author(s)
- Natascha Riahi
- Abstract
We show how the Laplace transform can be used to give a solution of the time-dependent Schrödinger equation for an arbitrary initial wave packet if the solution of the stationary equation is known. The solution is obtained without summing up eigenstates nor do we need the path integral. We solve the initial value problem for three characteristic piecewise constant potentials. The results give an intuitive picture of the wave packet dynamics, reproducing explicitly all possible reflection and transmission processes. We investigate classical and quantum properties of the evolution and determine the reflection and transmission probabilities.
- Organisation(s)
- Gravitational Physics
- Journal
- Quantum Studies: Mathematics and Foundations
- Volume
- 4
- Pages
- 103-126
- No. of pages
- 24
- ISSN
- 2196-5617
- DOI
- https://doi.org/10.1007/s40509-016-0087-5
- Publication date
- 2017
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103019 Mathematical physics
- Keywords
- ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics, Mathematical Physics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/15bfa512-176c-473f-babd-13e3d8c08442