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Visualization of Wave Functions Using Mathematica

P. Lang
M. Towns
Journal / Anthology

Journal of Chemical Education
Year: 1998
Volume: 75
Issue: 4
Page range: 506-509

As the above quatrain describes, even early researchers in quantum mechanics were puzzled over the nature of psi. Simply put, quantum mechanics involves a lot of symbolic-level representation. What these symbols mean is not a trivial question, and in fact, it is a question often asked by under-graduate physical chemistry students. How can we help these students understand psi, and |psi|^2? Initially students ask for information related to the concepts from classical physics with which they are acquainted. As Schrödinger said (1), "We have taken over from previous theory the idea of a particle and all the technical language concerning it. This idea is inadequate. It constantly drives our mind to ask for information which has obviously no significance." We have found that graphics generated using Mathematica (2) provide students with a greater understanding of the wave function psi and the probability density |psi|^2. In particular, the graphics focus student's attention on Born's statistical interpretation of psi which allows one to calculate the probability of finding a particle in a particular volume element. The laboratory activity that we constructed focuses on the models for translational, vibrational, and rotational motion - the two-dimensional particle in a box, the harmonic oscillator, and the particle on a sphere (3,4). Student understanding and achievement was measured using a post-lab survey, an examination question, and a question on the semester final. Results of these instruments are reported to draw attention to the experiences of the student.

*Science > Chemistry