Springer LINK: The Chemical Educator

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 30 (2025) pp 1-11

Interactive Animation of Time-Dependent Wavefunctions with Applications to Transitions

Matthew G. Marmorino

Department of Chemistry and Biochemistry, Indiana University South Bend, South Bend, IN 46615, mmarmori@iu.edu
Received January 29, 2024. Accepted February 27, 2024.

Published: 14 January 2025

Abstract. We introduce, and provide suggestions for using, a freely-available Mathematica project designed to explore five concepts of time-dependent wavefunctions using a one-dimensional particle in a box as a model system: (i) Complex nature and ambiguity of the normalization constant; (ii) Temporal oscillation of the real and imaginary components of a stationary-state wavefunction; (iii) Temporal oscillation of the probability density and the position expectation value áxñ for binary superpositions of stationary states; (iv) Selection rules for photon absorption and emission; (v) Physical meaning of the transition dipole moment.

Key Words: In the Classroom; physical chemistry; quantum mechanics; time dependence; transition dipole moment; stationary states; superpositions; transitions; Bohr frequency condition

(*) Corresponding author. (E-mail: mmarmori@iu.edu )

Article in PDF format(657 KB) HTML format

Supporting Materials:

The Mathematica project is available in the two forms below from the Chemical Educator. In each case, the file provides the user with a short description of the project and the controls that the user can manipulate. Both files require that “Dynamic Updating” be enabled. If this is not the default setting then the user may see the warning “This file contains potentially unsafe dynamic content” next to a button to “Enable Dynamics”. The first file, Time-Dependence-CE-MGM-Mathematica.nb is to be run by Mathematica which is available only to licensed users. The second file, Time-Dependence-CE-MGM-Wolfram-Player.nb is is to be run by Wolfram Player which is freely available as a download at https://www.wolfram.com/player. Wolfram Player allows the user to run certain types of pre-existing Mathematica files, but does not allow the user to edit or create files. (892 KB)