Learning Exercise
Self-Checked Problem Set: One-Dimensional Systems (Griffiths Chapter 2)
- Material:
- Quantum Mechanics - Free Graduate-Level Course
- Date last modified:
- September 25, 2026
- Created by:
- Bertrand Mercier des Rochettes
- License:
-
A graduate quantum mechanics course running from the mathematical foundations to advanced topics: Hilbert spaces, linear... see more
Exercise
A two-week problem set on stationary states in one dimension, built so students get immediate feedback without the instructor grading drafts.
Week 1 — Analytic work. Assign six problems from chapter 2 of Griffiths' Introduction to Quantum Mechanics (3rd edition), spanning the infinite square well, the finite well and the harmonic oscillator. Students attempt each one before looking at anything else. (Students need their own copy of the text for the problem statements.)
Week 1, second half — Self-check. For each problem, students watch the worked video solution on its own page at courseshub.world/quantum-mechanics/griffiths-solutions and write a short "divergence note": where their method differed from the video's, whether that difference was an error or a legitimate alternative route, and what they would do differently. Three or four sentences per problem.
Week 2 — Numerical confirmation. Using the browser-run Python programs at courseshub.world/quantum-mechanics/programs, students vary the width of the infinite square well and the frequency of the harmonic oscillator, and confirm two of their analytic results numerically. They record one prediction made before running the program, and whether it held.
Submission. The divergence notes, the numerical work with the prediction recorded in advance, and one closing paragraph naming which of the four systems they now find least intuitive and what specifically is unclear.
Assessment. Graded on diagnosis, not on correctness — the worked solutions are public, so grading answers measures nothing. Divergence notes 40% (is the error actually located, and is a mistake correctly distinguished from a valid alternative method?); numerical work 25% (was the prediction recorded before running the program, and is the comparison honest where it failed?); the analytic attempts 20% (method and clarity, not final answers); closing paragraph 15% (is the stated difficulty specific and real?).
A student who solves every problem correctly and writes "no divergence" six times scores poorly. That is deliberate: the skill being assessed is reading one's own reasoning critically.
Prerequisites: calculus through partial differential equations, linear algebra, complex numbers. Time required: two weeks, roughly 8-10 hours of student work.
Disciplines
Technical Notes
Everything runs in a modern browser on desktop or tablet. The simulations are Python executed client-side via Pyodide, so nothing is installed and no server-side account exists; the first run takes a few seconds to load the interpreter. Equations are typeset with MathJax. Video solutions are embedded from YouTube, so the exercise needs a connection that allows it — each one also links out to its source if embedding is blocked on a campus network.
Requirements
Prerequisites: calculus through partial differential equations, linear algebra, and complex numbers.
Students need their own copy of Griffiths, Introduction to Quantum Mechanics (3rd edition) for the problem statements. Problems are cited here by number only; the worked solutions, course material and activity design are supplied free.
No software to install — the programs run in the browser, and no account is needed to read anything on the site.
Topics
Time-independent Schrödinger equation; stationary states; infinite square well; finite square well; quantum harmonic oscillator (analytic and ladder-operator methods); free particle; normalisation; expectation values and uncertainty; numerical solution of eigenvalue problems; self-assessment and error diagnosis.
Type of Task
Learning Objectives
Assessment
Graded on diagnosis, not on correctness. The worked solutions are public, so grading answers measures nothing.
40% — Divergence notes: is the error actually located, and is a genuine mistake correctly distinguished from a legitimate alternative method?
25% — Numerical work: was the prediction recorded before running the program, and is the comparison honest where it failed?
20% — The analytic attempts: method and clarity, not final answers.
15% — Closing paragraph: is the stated difficulty specific and real?
A student who solves every problem correctly and writes "no divergence" six times scores poorly. That is deliberate — the skill being assessed is reading one's own reasoning critically, which is what makes the rest of the course survivable.