Spectrum of a Particle in a 1D Box

It is safe to say that every physical chemistry course teaches the Particle in a Box problem as an introduction to quantum mechanics. I have taught it also in my course for years.

I have been bothered for years, however, by the fact that the text books stop after solving the Schrodinger equation. All of them that we have surveyed do this. McQuarrie, Atkins, Engel, Levine, etc.

This is a shame because we can’t detect the energy levels by themselves. Quantum theory was invented to explain spectroscopy. So why not take the 1D Particle in a Box (1DPB) problem all the way to a simulated spectrum?

At SHSU, we do.

Here are three lectures that explain what I do with the Particle in a Box.

(Be patient with the Kahoot quizzes and end of class Q&A. Feel free to skip ahead, or try to answer the questions in your own mind to see how you do! To find all my Kahoot content search for my username chem_prof on Kahoot. I have Quantum, Thermo, and Forensic Chem Kahoots.)

Lecture 1 – Managing the Messy Mathematics

This lecture takes the spectrum of a 1DPB apart to show what pieces of the spectrum are explained by quantum theory.

Lecture 2 – The Schrodinger Equation

This lecture is the traditional presentation of the 1DPB problem – normalizing the wave functions and solving for the energies via the Schrodinger equation.

Lecture 3 – Spectral Transitions and Spectral Assignments

This lecture discusses spectral transitions, the transition moment integrals and the transition equation which tells us about the spacing of our spectral lines. The transition equation also tells us about the quantum system if we begin with an experimental spectrum and assign the quantum transitions.

What are your reactions to this approach? I’d love to hear from you in the comments section. I am preparing this material for a book for students to read in the summer prior to taking pchem. I think it will greatly help to get them thinking about our quantum world early and often.

Happy Pchemming!

Darren Williams

P.S. This is tagged under research, because a survey of the literature has revealed that these simple (ish) 1D examples have not been published.