by

Todd Timberlake

Associate Professor of Physics & Astronomy

Berry College

Mount Berry, GA

I teach the course using interactive methods. Students work in small groups (usually 2) to complete worksheet-based tutorials during class time. Occasionally I lecture or demonstrate something using computer software. Students also do fairly typical homework problems, and complete their writing assignments, on their own.

- Syllabus: provides a general description of the course and a schedule of topics to be discussed.

You are free to use (and even change) the worksheets, but please see the Terms of Use before doing so. If you wish to edit the worksheets, and you know how to use LaTeX (or are willing to learn), you can download a package containing all the .tex files and other necessary files (images, etc.) for all of the worksheets. To download this package click the link below:

ActiveQuantumTex.zip.

If you would like to edit the worksheets but need them in a different format please email me (ttimberlake@berry.edu) and I may be able to accommodate you.

Please watch out for typos and other errors in these handouts. I
cannot guarantee that they are without flaws - but the handouts
posted here are all materials that I have used in my own class.
Please work carefully through the exercises yourself before you give
them to your students! Finally, I apologize for the fact that some
of the notes are just scanned copies of hand-written pages. I
promise to convert these into LaTeX the next time I teach the course.

Topic | Griffiths Sections | Worksheet |
---|---|---|

Schrodinger Equation Notes | 1.1-1.2 | 1SchrodingerEqution.pdf MathTips.pdf |

Probability and Prediction | 1.3-1.4 | PredictingProbabilities.pdf |

Momentum and Uncertainty | 1.5-1.6 | MomentumUncertainty.pdf |

Energy Eigenvalue Problem Notes | 2.1 | 2EnergyEigenvalueProblem.pdf PhysicalityConditions.pdf |

Infinite Square Well | 2.2 | InfiniteSquareWell.pdf |

Infinite Square Well Notes | 2.2 | 3InfinitSquareWellNotes.pdf |

Properties of Bound States | NA | BoundStates.pdf |

Harmonic Oscillator (Series Solution) | 2.3 | HOseries.pdf |

Harmonic Oscillator (Commutators and Ladder Operators) | 2.3 | HOoperators.pdf |

Harmonic Oscillator (Algebraic Solution) | 2.3 | HOalgebraic.pdf |

Free Particle Notes | 2.4 | FreeParticleNotes.pdf |

Free Particle | 2.4 | FreeParticle.pdf |

Delta Well | 2.5 | DiracDelta.pdf |

Finite Square Well | 2.6 | FiniteSquareWell.pdf |

Finite Square Well Notes | 2.6 | 4FiniteWellNotes.pdf Finite Well Maxima Notebook (zipped) |

Scattering I: the Delta Well | 2.6 | ScatteringI.pdf |

Scattering II: the Step | 2.6 | ScatteringII.pdf |

Dirac Notation Notes | 3.1 | DiracNotation.pdf |

Dirac Notation | 3.1 | DiracNotation.pdf |

Observables and Operators | 3.2-3.3 | Operators.pdf |

Hermitian Operators Notes | 3.3 | 5UsefulBases.pdf 6EigenstatesHermitian.pdf |

Statistical Interpretation | 3.4 | Probabilities.pdf |

Generalized Uncertainty Principle | 3.5 | GenUncertainty.pdf |

Using Dirac Notation | 3.6 | UsingDiracNotation.pdf |

Spherically Symmetric Potentials Notes | 4.1 | 7SphericalHarmonics.pdf Spherical Harmonics Maxima Notebook (zipped) |

Spherical Harmonics | 4.1 | SphericalHarmonics.pdf |

Hydrogen Atom I | 4.2 | Hydrogen.pdf |

Hydrogen Atom II | 4.2 | Hydrogen2.pdf |

Angular Momentum | 4.3 | AngularMomentum.pdf |

Angular Momentum and Spin Notes | 4.3-4.4 | SpinNotes.pdf |

Spin | 4.4 | Spin.pdf |

Spin in Maxima | 4.4 | Spin Matrices Maxima Notebook (zipped) |

Electron in a Magnetic Field | 4.4 | BFieldTutorial.pdf |

Addition of Angular Momentum | 4.4 | AddingAngularMomentum.pdf |

Identical Particles | 5.1 | IdenticalParticles.pdf |

Exchange Forces | 5.1 | ExchangeForces.pdf |

Perturbation Theory Notes | 6.1 | NDPTnotes.pdf |

Non-degenerate Perturbation Theory | 6.1 | NDPT.pdf |

Degenerate Perturbation Theory | 6.2 | DegPT.pdf |

Degenerate Perturbation Theory in Maxima | 6.2 | Degenerate Perturbation Theory Maxima Notebook (zipped) |

**Long Paper:**This assignment focuses on the Stern-Gerlach experiment. The goal is to show students how the results of experiments force us into some of the strange ideas of quantum mechanics. Students conduct their own experiments using the SPINS program (originally created by Schroeder and Moore) and interpret the results.- Long Paper Assignment
- Long Paper JAR file: this JAR file contains both the SPINS Java program as well as the curricular materials for conducting the required experiments for the Long Paper assignment.
- Peer Review Instructions
- Rewrite Instructions

**Short Paper 1**: This assignment focuses on the double-slit experiment. Students respond to John Wheeler's analysis of the double-slit experiment in his article "Law without law" (see below). This paper forces students to confront the "measurement problem" in quantum mechanics.**Short Paper 2**: This assignment focuses on an experimental verification of decoherence using thermal emission from buckyballs conducted by Anton Zeilinger and colleagues. Students are asked to analyze the experimental data to determine whether or not this experiment constitutes a clear demonstration of decoherence. They are then asked how decoherence applies to the behavior of macroscopic systems (like Schrodinger's Cat).**Old Short Paper 2**: This assignment focuses on the EPR experiment. Students read an article by Alain Aspect on recent experimental verifications of the violation of Bell's Inequality. The writing assignment forces students to address the possible conclusions that can be drawn in light of these experiments, and also to evaluate which of these conclusions is the most sensible (in their own view). [Note: I regretfully no longer use this assignment. I just can't fit it in along with everything else. What is listed as Short Paper 2 above used to be Short Paper 3, back when I still used this assignment.]**Brief Essays**: This document lists a series of brief essay questions that are used to ensure that students keep up with their reading and think about what they have read. These questions deal with material from Lindley's*Where does the weirdness go?*(see below).

- David Lindley,
*Where does the weirdness go?*(Basic Books, 1996). - SPINS applet: available
online. See also Schroeder and Moore, "A computer-simulated Stern-Gerlach laboratory,"
*American Journal of Physics***61**, 798-805 (1993). - John Wheeler, "Law without law," in
*Quantum Theory and Measurement*ed. by Wheeler & Zurek (Princeton Univ. Press, 1983). - Alain Aspect, "Bell's inequality test: more ideal than ever,"
*Nature***398**, 189-190 (1999). - Lucia Hackermuller, Klaus Hornberger, Bjorn Brezger, Anton Zeilinger, and Markus Arndt, "Decoherence by the emission of thermal radiation" available online.

All
of the curricular materials listed on this page are copyrighted by Todd Timberlake and are licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. You may modify and redistribute these materials for non-commercial use as long as you clearly cite the original author (Todd Timberlake) and release the materials under the same license.

- "Turning Quantum Mechanics Course Notes into Tutorials," invited
talk given at the
*2011 Summer Meeting of the American Association of Physics Teachers*, Omaha, NE, August 2011. Click here for slides from my talk. - "Writing-Intensive Quantum Mechanics,"
talk given at the
*2006 Winter Meeting of the American Association of Physics Teachers*, Anchorage, AL, January 2006. Click here for slides from my talk.

Todd K. Timberlake (ttimberlake@berry.edu)