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://ucris.univie.ac.at/portal/en/publications/solving-the-timedependent-schroedinger-equation-via-laplace-transform(15bfa512-176c-473f-babd-13e3d8c08442).html