PHYS307 (Intermediate Quantum Mechanics) Fall 2014
Scott Heinekamp (scotth@wells.edu) Stratton 302 ext 3361
(http://morgan.wells.edu/faculty/scotth)

Course Content
This is an advanced course in Physics, often abstract and heavily mathematical. Let's hope that the mathematics never obscures the important physics that we uncover. We start with a thorough grounding in QM of single-body systems, and then move on to applications (via some statistical mechanics) to important many-body problems. In a sense, what we'll take on will be a much more mathematical handling of what was introduced in PHYS302 (Modern Physics), where the goal was to understand the hydrogen atom. Here, we'll spend effort on multi-particle systems by the end, seeing how compromises have to be made in order to handle quantum particle-particle interactions, and learn about fruitful ways to approximately solve (in some sense) the equations of QM.
Quantum physics, which can sometimes be regarded as the theory of the very small, is a very big subject! We begin with "wave mechanics", which was the approach used in 302 (and so you'll recall a lot of modern physics, and Tipler & Llewellyn's Modern Physics or the equivalent will serve as a very useful reference to help you in remembering that material, as well as other topics along the way). Motivated by the crucially important 'harmonic oscillator' potential energy, we'll move on to a more abstract "operator" focus, where the mathematics is in many ways simpler, while at the same time being more abstract. The statistical mechanics is easiest to handle in the operator language, while the approximations are most suited to wave mechanics.
There are many fine textbooks on quantum mechanics. Go to the library and look over our collection, and take out one or a few for your personal use. I'll put together a list of suggested books soon. For our text, we will use Griffiths's Quantum Mechanics (2th edition), which does not shirk from doing hard mathematics at any point, but which keeps the focus on the physics at all times. It's a very lively book, and very reader-friendly. One book in particular, Reed's Quantum Mechanics, will be put on reserve in the Stratton reading room (and where it must stay so all can access it!!). This book is new, and has as its greatest virtues simplicity and clarity -- but it is too elementary to really get at the challenging stuff that we want to include in a course such as this.

Lecture Schedule and Griffith's Readings

Week .5 (partial week of 28 Aug) (Your Favorite Modern Physics Book) Motivation for quantization: the hydrogen spectrum.
  • Powerpoint 0: Motivation
    Week 1.5 (week of 1 Sep) (1.3) Basic ideas about probability and averaging. (YFMPB) Further motivation for quantization: the black body. (1.1-1.2,1.4-1.6) The TDSE (Time-Dependent Schrodinger Equation), as motivated by the free wavicle. The uses of the wavefunction.
  • Powerpoint I: Probability
  • Powerpoint II: Schrodinger
    Week 2.5 (week of 8 Sep) (2.1-2.2) The TISE (Time-Independent Schrodinger Equation). Stationary states. Infinite square well. Fourier's 'trick' (2.6) Qualitative approach to the finite square well. Bound and free states. Reflection and transmission.
  • Powerpoint III: Energy Eigenstates
  • Powerpoint IV: Infinite 1d Square Well
  • Powerpoint V: Finite 1d Square Well
    Week 3.5 (week of 15 Sep) (2.3 intro, 2.3.2) Harmonic oscillator (analytic approach). (2.5) The Dirac delta function potential.
  • Powerpoint VI: Harmonic Oscillator: Analytic Approach
  • Powerpoint VII: Delta Function Potential
    Week 4.5 (week of 22 Sep) (2.4) Various aspects of formal quantum mechanics. Phase speed and group speed. The free wavicle and the wave packet.
  • Powerpoint VIII: Packets and Free Particles
    Week 5.5 (week of 29 Sep) (2.3.1) Harmonic Oscillator: algebraic approach.
  • Powerpoint IX: Harmonic Oscillator: Algebraic Approach
    Exam I
  • Solutions to Exam I
    Week 6.5 (week of 6 Oct) (4.1) Review of spherical coordinates. 3d quantum mechanics. Spherically symmetric potentials.
  • Powerpoint XI: Three Dimension
    Week 7 (partial week of 15 Oct) The angular dependence of the wavefunction.
    Week 8 (week of 20 Oct) (4.3) Orbital angular momentum.
  • Powerpoint XII: Angular Momentum
    Week 9 (week of 27 Oct) (4.2) The radial equation. The hydrogen atom.
  • Powerpoint XIII: Radial Equation
    Exam II
    Week 10 (week of 3 Nov) (YFMPB) Chemist's orbitals. (4.4 intro, 4.4.1) Spin angular momentum.
    Week 11 (week of 10 Nov) (4.4.3) Combining angular momenta.
    Week 12 (week of 17 Nov) (5.1) Two-particle wavefunctions. Identical particles. Bosons or Fermions? Exchange 'forces'. (5.2) Atoms. Hund's rules.
  • Powerpoint XIV: Spin and Angular Momentum Addition
    Week 13 (week of 1 Dec) make-up for exam II
    Week 14 (partial week of 8 Dec) (5.2) Atoms and Spectroscopic notation. Hund's rules. The periodic table.
  • Powerpoint XV: Atoms and Term Symbols

    Rules of the Game
    Attendance is expected at every lecture, as is showing up punctually, so that we can make best use of the time. I expect that you will have read the material BEFORE the class, to maximize the value of the lecture and discussion. Of course, you are encouraged to bring questions to class, where all class members will benefit from our conversation about the subtleties of QM. Your grade will be influenced by the level of participation in class. It goes without saying (but I'll say it anyway) that cell phones are to be turned off, and no laptops may be used except for taking notes, or perhaps the occasional accessing of some on-line resource (of which there are many, for since physicists INVENTED the internet, some of the material there concerning physics is really quite good).

    Grading in this course
    Homework/class participation (30%):
    The set of homework assignments may be found at Homework Assignment.
    Tests (50%): 3 of them, 20% each except that the lowest score is weighted 10%
    Final Exam (20%): only factored in if it raises your average
    This syllabus (web address http://morgan.wells.edu/faculty/scotth/ph307/ph307syl.htm), is the course's home page.