Applied Quantum Mechanics Assignments

Oberlin College Physics 412

Spring 2012

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 9 March 2012.

Applied 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 Friday, 10 February):

• Physics of QM problem 15.1: Quantal recurrence in the infinite square well
• Physics of QM problem 15.2: Quantal recurrence in the Coulomb problem
• Physics of QM problem 15.3: Atomic units
• Physics of QM problem 15.4: 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, 17 February):

• Read Griffiths section 7.1 on the variational principle.
• Read Griffiths section 5.1 on two-particle systems.
• Read Griffiths section 5.2.1 on Helium.
• Read Griffiths section 7.2 on the ground state of Helium.
• Physics of QM problem 16.1: The Stark effect

Model Solutions 2:

• The Stark effect (PDF)

Assignment 3 (due Friday, 24 February):

• Read Griffiths section 4.4 (omit 4.4.2) on spin and the addition of angular momenta.
• Read Griffiths section 5.2 on atoms.
• Physics of QM problem 15.5: Variational principle for the harmonic oscillator.
• Physics of QM problem 14.10: Mean separation.
• Physics of QM problem 14.11: Building basis states.
• Physics of QM problem 14.12: Electron-electron repulsion.
• Physics of QM problem 14.13: Two-electron ions.

Model Solutions 3:

• Variational principle for the harmonic oscillator (PDF)
• Mean separation (PDF)
• Building basis states (PDF)
• Electron-electron repulsion (PDF)
• Two-electron ions (PDF)

Assignment 4 (due Friday, 2 March):

• Read Griffiths section 7.3 on the hydrogen molecule ion.
• 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.
• Griffiths problems 4.34, 4.35, and 4.36: Addition of angular momenta.
• Griffiths problems 5.12 and 5.13: Atoms.
• Physics of QM problem 19.1: Evaluation of integrals.
• Physics of QM problem 19.2: Thinking about integrals.

Model Solutions 4:

• Addition of angular momenta (PDF)
• Atoms (PDF)
• The hydrogen molecule ion (PDF)
• Spreadsheet for the hydrogen molecule ion (excel)

Assignment 5 (due Friday, 9 March):
Exam: The problems below constitute an unlimited-time take-home exam due Friday, 9 March, at 11:00 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.

• Read Griffiths chapter 8 on the WKB approximation.
• Griffiths problem 8.2: Alternative derivation of WKB.
• Griffiths problems 8.5 and 8.6: The quantum bouncer.
  Omit 8.5(d) and 8.6(c).
• Griffiths problem 8.14: 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 335-339.]

Model Solutions 5 (PDF)

Assignment 6 (due Friday, 23 March):

• Read Griffiths chapter 9 on time-dependent perturbation theory. (Particularly section 9.2.3 on incoherent light and the rate equation.)
• Griffiths problem 9.1: Matrix elements.
• Griffiths problem 9.11: 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 9.14 (a) and (b).
• [In addition, look at but don't execute Griffiths problem 9.21.]

Model Solutions 6 (PDF)