Quantum Mechanics and Electrodynamics Assignments

Fall 2024

This World Wide Web page written by Dan Styer, Oberlin College Department of Physics and Astronomy ;
http://www.oberlin.edu/physics/PrivateReading/Assignments/assignments.html;
last updated 4 October 2024.

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

"The Physics of QM" means Daniel F. Styer, The Physics of Quantum Mechanics edition of 3 September 2024.

Assignment 1 (due Thursday, 12 September):

• Read The Physics of QM, section 17.2, "Scaled variables".
• Read The Physics of QM, section 18.1, "The Stark effect".
• Physics of QM problem 17.1: Quantal recurrence in the infinite square well
• Physics of QM problem 17.3: Atomic units
• Physics of QM problem 17.4: Scaling in the stadium problem

Model Solutions 1:

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

Assignment 2 (due Thursday, 19 September):

• Read Griffiths section 8.1 on the variational principle.
• Read The Physics of QM, section 17.3, "Variational method for the ground state energy".
• Read 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 19, "Helium".
• Physics of QM problem 18.1: The Stark effect

Model Solutions 2:

• The Stark effect (PDF)

Assignment 3 (due Thursday, 26 September):

• 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 20, "Atoms".
• Physics of QM problem 17.5: Variational principle for the harmonic oscillator.
• Physics of QM problem 15.7: Mean separation in the infinite square well.
• Physics of QM problem 15.11: Building basis states for three particles.

Model Solutions 3:

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

Assignment 4 (due Thursday, 3 October):

• Read Griffiths section 8.3 on the hydrogen molecule ion.
• Read The Physics of QM, chapter 21, "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 15.18: 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 Thursday, 10 October):

• Read Griffiths chapter 9 and Physics of QM chapter 22 on the WKB approximation.
• Physics of QM problem 21.1: The hydrogen molecule ion: Evaluation of integrals.
• Physics of QM problem 21.2: 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 Thursday, 17 October):

• Physics of QM problem 22.2: Alternative derivation of WKB.
• 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 (optional):

• 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 23, "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 17.3, "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)

FALL BREAK

Assignment 8 (PDF) (Due Thursday, 31 October.)

Model Solutions 8:

• Magnetic force between two moving charged particles
• Griffiths 7.8: Electric induction
• Griffiths 7.9: Apparent oversight in the flux rule
• Griffiths 7.15: Solenoid
• Griffiths 7.25: Inductance of a hairpin loop

Assignment 9 (PDF) (Due Thursday, 7 November.)

Model Solutions 9:

• Magnetic energy and electric generators
• Griffiths 7.37: A solution to the Maxwell equations
• Griffiths 7.39: Experimental detection of magnetic monopoles
• Griffiths 7.42: Electrostatics of a circuit
• Mark Heald's article that inspired the above problem. (Nice pictures!)

Assignment 10 (PDF) (Due Thursday, 14 November.)

Model Solutions 10:

• Griffiths 7.2: Energy in capacitor discharge
• Griffiths 7.34 and 8.2: Capacitor fields and energy
• Griffiths 7.63: Alfven's theorem
• Griffiths 8.19: Thomson's dipole

Assignment 11 (PDF) (Due Thursday, 21 November.)

Model Solutions 11:

• Griffiths 9.12: Time averages
• Griffiths 9.13: Maxwell stress tensor for light
• Griffiths 9.23: Water waves and quantal waves

Assignment 12 (PDF) (Due Thursday, 5 December.)

Model Solutions 12:

• Griffiths 10.3: Potentials and gauges
• Griffiths 10.16: Potential of a moving point charge
• Griffiths 11.15: Headlamp effect

Assignment 13 (PDF) (Due never.)

Model Solutions 13:

• Units in electromagnetism
• Field energy and momentum

Sample Final/Honors Exam (PDF)