# Quantum Mechanics Assignments

## Fall 2023

This World Wide Web page written by Dan Styer, Oberlin College Department of Physics and Astronomy ;
http://www.oberlin.edu/physics/dstyer/QM/Assignments/assignments.html;
last updated 17 November 2023.

Unless otherwise noted, these problems appear in my draft textbook The Physics of Quantum Mechanics.

Assignment 1: (Due Wednesday, 13 September.)

• There are quite a few problems in this assignment, but each one is pretty short.
• Problem 3.11: The trace
• Problem 3.12: The outer product
• Problem 1.2: Exit probabilities
• Problem 1.5: Tilted analyzer loop
• Problem 1.6: Three analyzer loops
• Problem 1.7: Bomb-testing interferometer

Model Solutions 1:

Assignment 2: (Due Wednesday, 20 September.)

• Problems 3.1 through 3.4, inclusive: Photon polarization
• Problem 3.13: Pauli matrix algebra

Model Solutions 2:

Assignment 3: (Due Friday, 29 September.)

• You may want to read pages 1 through 70 of Daniel T. Gillespie, A Quantum Mechanics Primer, at this link. Caution: Gillespie treats only systems with an infinite number of basis states, he does not distinguish between a state |ψ> and its representation ψ(x), and he uses the notation (φ,ψ) for what Dirac would call <φ|ψ>.
• (Problems below from the version of The Physics of Quantum Mechanics dated 22 September 2023.
• Exercises 3.5 ("Prove the Schwarz inequality"), 3.10 and 3.11 ("Eigenproblem for functions of operators").
• Exercises 4.3 ("Interpretation of amplitude squared as a probability"), 4.4 ("Mean values"), 4.10 ("Measurement example"), 4.12.

Model Solutions 3:

Assignment 4: (Due Friday, 6 October.)

• Take home exam. Topics: The phenomena of quantum mechanics: quantization, interference, and entanglement. Mathematical tools: amplitude, states, outer products, operators. Formalism: linear algebra, formal statements.
• Sample exam (PDF)
• Model solutions for sample exam (PDF)

Model Solutions 4:

Assignment 5: (Due Friday, 13 October.)

• Problem 5.3: Ammonia molecule: position of nitrogen atom
• Problem 5.4: Ammonia molecule in an electric field

Model Solutions 5:

Fall Break

Assignment 6: (Due Friday, 27 October.)

• Physics of QM problems 6.6 through 6.10, inclusive.

Model Solutions 6:

Assignment 7: (Due Friday, 3 November.)

• Physics of QM problems 8.2 through 8.5, inclusive.

Model Solutions 7:

Assignment 8: (Due Friday, 10 November.)

Model Solutions 8:

Assignment 9: (Due Friday, 17 November.)

• Physics of QM (version of 10 November 2023) problems 10.2, 10.3, and 10.4.

Model Solutions 9:

Assignment 10: (Due Friday, 1 December.)

• Physics of QM problems 11.2, 11.3, 11.5, and 11.6.

Model Solutions 10:

Assignment 11: (Due Wednesday, 8 December.)

• Physics of QM problems 13.1, 13.2, and 13.3.
• Physics of QM problem 14.1. (You should also look at, but not work, problem 14.4, "Virial theorem".)

Model Solutions 11:

Final Exam: