Solving the time-dependent Schrödinger equation via Laplace transform

Autor(en)

Natascha Riahi

Abstrakt

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(en)

Gravitationsphysik

Journal

Quantum Studies: Mathematics and Foundations

Band

4

Seiten

103-126

Anzahl der Seiten

24

ISSN

2196-5617

DOI

https://doi.org/10.1007/s40509-016-0087-5

Publikationsdatum

2017

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Atomic and Molecular Physics, and Optics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/15bfa512-176c-473f-babd-13e3d8c08442