Quantum Mechanics Assignments

Oberlin College Physics 312

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 22 September 2023.

Quantum Mechanics home page

Technical note: To access the links marked (PDF) you must first download the free Adobe Acrobat Reader or Open Standard software.

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:

• Problems 3.11 and 3.12: Matrix calisthenics (PDF)
• Problem 1.2: Exit probabilities (PDF)
• Problems 1.5, 1.6, and 1.7: Concerning Interference (PDF)

Assignment 2: (Due Wednesday, 20 September.)

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

Model Solutions 2:

• Problems 3.1 through 3.4: Photon polarization (PDF)
• Problem 3.13: Pauli matrix algebra (PDF)

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:

• Exercises on linear algebra (PDF)
• Exercises on formalism (PDF)

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:

• Model solutions for exam (PDF)

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:

• Ammonia (PDF)

Fall Break

Assignment 6: (Due Friday, 27 October.)

• Physics of QM problems 6.6 through 6.10, inclusive.

Model Solutions 6:

• Problems 6.6 through 6.10: Continuum systems (PDF)