Applied Quantum Mechanics Private Reading Assignments

Fall 2021

This World Wide Web page written by Dan Styer, Oberlin College Department of Physics and Astronomy ;
http://www.oberlin.edu/physics/dstyer/AppliedQM/Assignments/assignments.html;
last updated 19 August 2021.

"Griffiths" means David J. Griffiths and Darrell F. Schroeter, Introduction to Quantum Mechanics third edition (Cambridge University Press, 2018, red-brown cover).

Assignment 1 (due Friday, 8 October):

• Read The Physics of QM, section 16.1, "Scaled variables".
• Read The Physics of QM, section 17.1, "The Stark effect".
• Physics of QM problem 16.1: Quantal recurrence in the infinite square well
• Physics of QM problem 16.2: Quantal recurrence in the Coulomb problem
• Physics of QM problem 16.3: Atomic units
• Physics of QM problem 16.4: Scaling in the stadium problem

Model Solutions 1:

• Quantal recurrence in the infinite square well (PDF)
• Quantal recurrence in the Coulomb problem (PDF)
• Atomic units (PDF)
• Scaling in the stadium problem (PDF)

Assignment 2 (due Friday, 15 October):

• Read Griffiths section 8.1 on the variational principle.
• Read The Physics of QM, section 16.2, "Variational method".
• Read Invitation to QM, chapter 6, "Identical Particles".
• Dip into The Physics of QM, chapter 15, "Identical Particles".
• Read Griffiths section 5.1 on two-particle systems.
• Read Griffiths section 5.2.1 on Helium.
• Read Griffiths section 8.2 on the ground state of Helium.
• Read The Physics of QM, chapter 18, "Helium".
• Physics of QM problem 17.1: The Stark effect

Model Solutions 2:

• The Stark effect (PDF)

Assignment 3 (due Friday, 22 October):

• Read Griffiths section 4.4 (omit 4.4.2) on spin and the addition of angular momenta.
• Read Griffiths section 5.2 on atoms.
• Read The Physics of QM, chapter 19, "Atoms".
• Physics of QM problem 16.5: Variational principle for the harmonic oscillator.
• Physics of QM problem 15.10: Mean separation.
• Physics of QM problem 15.11: Building basis states.

Model Solutions 3:

• Variational principle for the harmonic oscillator (PDF)
• Mean separation (PDF)
• Building basis states (PDF)

Assignment 4 (due Friday, 29 October):

• Read Griffiths section 8.3 on the hydrogen molecule ion.
• Read The Physics of QM, chapter 20, "Molecules".
• If you want to learn more about molecules, look also at:
  • Hermann Haken and H.C. Wolf, The Physics of Atoms and Quanta (Springer-Verlag, Berlin, 1996), fifth edition, chapter 23 ("chemical bonding"). Deemphasize sections 23.3, 23.6, and 23.8.
  • Gordon Baym, Lectures on Quantum Mechanics (W.A. Benjamin, Inc., Reading, Massachusetts, 1969), chapter 21 ("molecules"). Deemphasize pages 470-474.
• Physics of QM problem 15.13: Two-electron ions.
• Griffiths problems 4.37, 4.38, and 4.40: Addition of angular momenta.
• Griffiths problems 5.17 and 5.18: Atoms.

Model Solutions 4:

• Two-electron ions (PDF)
• Addition of angular momenta (PDF)
• Atoms (PDF)

Assignment 5 (due Friday, 5 November):

• Read Griffiths chapter 9 and Physics of QM chapter 21 on the WKB approximation.
• Physics of QM problem 20.1: The hydrogen molecule ion: Evaluation of integrals.
• Physics of QM problem 20.2: The hydrogen molecule ion: Thinking about integrals.

Model Solutions 5:

• The hydrogen molecule ion (PDF)
• Spreadsheet for the hydrogen molecule ion (excel)

Assignment 6 (due Friday, 11 November):
Exam: The problems below constitute an unlimited-time take-home exam due Friday, 11 November, at 9:00 am. You may use books, notes, calculators, tables of integrals, computer programs, internet searches, etc., but you may not collaborate, nor consult any person other than Dan Styer. You may do internet searches on things like "What are the zeros of the Airy function?" but not on things like "What is the solution to Griffiths problem 9.2?".

• Griffiths problem 9.2: Alternative derivation of WKB.
• Griffiths problems 9.6 and 9.7: The quantum bouncer.
  Omit 9.6(d) and 9.7(c).
• Griffiths problem 9.16: WKB for the Coulomb problem.
  Hint: Keep track of your signs to avoid taking the square root of negative numbers! Remember that E is a negative number.
• [In addition, look at but don't execute the other problems on Griffiths pages 371-375.]

Model Solutions 6 (PDF)

Assignment 7 (due Friday, 19 November):

• Read Griffiths chapter 11 on quantum dynamics through time-dependent perturbation theory. (Particularly section 11.2.3 on incoherent light and the rate equation.)
• Read Physics of QM chapter 22, "The Interaction of Matter and Radiation".
• Griffiths problem 11.2: Matrix elements.
• Griffiths problem 11.13: Decay times.
  Express this decay time in terms of the characteristic atomic time τ₀ found in assignment 1, Physics of QM problem 15.3, "Atomic units". If time were drawn out so that an atomic "orbit" lasted for one heartbeat, then how much time would this atomic decay require? What was the weather like this long ago?
• Griffiths problem 11.16 (a) and (b).
• [In addition, look at but don't execute Griffiths problem 11.31.]

Model Solutions 7 (PDF)