Quantum Mechanics, Physics 3220 Fall 97

My lecture notes will be photocopied, and made available in the Math/Phys library, and also outside my office. Here, I have provided a brief (usually one line) reminder of the highlights of each lecture. (More detailed notes will be available for the first few lectures as well) Please let me know if you think this is of any use, feedback is welcome!

Brief summary of lectures

Gas. Ch. 1

Lecture 1:
Mon, Aug. 25, 1997
Introduction, discussion of syllabus. (What is quantum mechanics about, where does it come from?)
There are detailed notes available for this lecture.

Lecture 2:
Wed, Aug. 27, 1997
Derivation of Rayleigh-Jeans, and Planck's insight. Einstein and the photoelectric effect, + a few convenient numbers. Compton effect (kinematics, including brief review of relativity formulas.)
There are detailed notes available for this lecture

Lecture 3:
Fri, Aug. 29, 1997
Finished Compton, discussed De Broglie, Davisson and Germer, and the Bohr model.
There are detailed notes available for this lecture.
(Mon, Sept. 1
Labor Day Holiday)
Gas. Ch. 2

Lecture 4:
Wed, Sept. 3, 1997
Wave Packets, Fourier transforms.
There are detailed notes available for this lecture.

Lecture 5:
Fri, Sept. 5, 1997
Time evolution of wave packets, intro to Schrodinger Eqn, intro to Heisenberg Uncertainty.
There are detailed notes available for this lecture.
Gas. Ch. 3

Lecture 6:
Mon, Sept. 8, 1997
Heisenberg Uncertainty Examples. Start Ch3, Interpretation of the Schodinger Eqn.
There are detailed notes available for this lecture.

Lecture 7:
Wed, Sept. 10, 1997
Probability interpretation, and probability currents. Expectation values.
There are detailed notes available for this lecture.

Lecture 8:
Fri, Sept. 12, 1997
Momentum expection, momentum space wave functions,operators.
There are detailed notes available for this lecture.
Gas. Ch. 4

Lecture 9:
Mon, Sept. 14, 1997
Commutators (examples), momentum is real (proof), linear operators, eigenvalues and eigenfunctions(eigenvectors), similarity between vectors and functions, Schrodinger eqn -> eigenvalue equation.
There are detailed notes available for this lecture.

Lecture 10:
Wed, Sept. 16, 1997
Schrodinger Eq'n as eigenvalue equation, solve for time dependence. Delta function "interlude". Solution to puzzle: the eigenfunctions of position are delta functions. Intro to particle in box.
There are detailed notes available for this lecture.

Lecture 11:
Fri , Sept. 19, 1997
Particle in a box - energy, eigenfunctions, and discussion. (Expansion, time dependence) Quiz (flux).
There are detailed notes available for this lecture.

Lecture 12:
Mon, Sept. 22, 1997
(Discussed quiz, and upcoming exam) Expansion, probability interpretation of c_n's, time dependence.
There are detailed notes available for this lecture.

Lecture 13:
Wed, Sept. 24, 1997
More expansion examples, expansion in momentum.
There are detailed notes available for this lecture.

Lecture 14:
Fri, Sept. 26, 1997
More discussion of momentum eigenfunctions, Parity.
There are detailed notes available for this lecture.
Gas. Ch. 5

Lecture 15:
Mon, Sept. 29, 1997
Review for exam. Start Gas Ch 5 - scattering from a potential. (Solved S.E., used continuity of u and u', found R and T)
There are detailed notes available for this lecture.

Lecture 16:
Wed, Oct. 1, 1997
Continue with Ch. 5: flux, variations on the step, and the "square well" scattering state solutions.
There are detailed notes available for this lecture.

Lecture 17:
Fri, Oct. 3, 1997
Finish the square "bump" (resonance transmission), and discuss tunneling including specific example of alpha decay.
There are detailed notes available for this lecture.

Lecture 18:
Mon, Oct. 6, 1997
Substitute lecture with John Taylor. More on Ch. 5 - Bound states of square well. (Some review as well)
There are detailed notes available for this lecture.

Lecture 19:
Wed, Oct. 8, 1997
Substitute lecture with John Taylor. Continue Ch. 5 - more on bound states of a finite square well. Set up the delta function potential.
There are detailed notes available for this lecture.

Lecture 20:
Fri, Oct. 10, 1997
Physics of delta function. Solution for energy of bound state, and scattering states (R and T) Set up "double delta function".
There are detailed notes available for this lecture.

Lecture 21:
Mon, Oct. 13, 1997
Finish double delta. Start harmonic oscillator
There are detailed notes available for this lecture.
Gas. Ch. 6 (Griff. Ch. 3)

Lecture 22:
Wed, Oct. 15, 1997
Finish harmonic oscillator (the "crude" way), start Gas. Ch. 6 (Formalism of quantum mechanics) Analogy between vectors and wave functions.
There are detailed notes available for this lecture.

Lecture 23:
Fri, Oct. 17, 1997
Quiz today. (Half - harmonic oscillator) Dirac notation, some linear algebra.
There are detailed notes available for this lecture.

Lecture 24:
Mon, Oct. 20, 1997
More Dirac notation, operators, Hermiticity.
There are detailed notes available for this lecture.

Lecture 25:
Wed, Oct. 22, 1997
More about operators and Hermiticity, some theorems about Hermitian operators.
There are detailed notes available for this lecture.

Lecture 26:
Fri, Oct. 24, 1997
The formal postulates of quantum, also discussion of degeneracy, and simultaneous eigenvalues.
There are detailed notes available for this lecture.

Lecture 27:
Mon, Oct. 27, 1997
Generalized uncertainty principle, and time dependence.
There are detailed notes available for this lecture.
Gas. Ch. 7

Lecture 28:
Wed, Oct. 29, 1997
Operator methods: Harmonic Oscillator
There are detailed notes available for this lecture.

Lecture 29:
Fri, Oct. 31, 1997
(Ghostly) conclusions to operator solution of Harmonic Oscillator. Time dependence of operators.
There are detailed notes available for this lecture.
(skip 8 for now - ) Gas. Ch. 9

Lecture 30:
Mon, Nov 3, 1997
Review of time dependence of operators. ( Finish Ch. 7) Summarize the start of Ch. 9, (Schrodinger Eq'n in 3-D) but we will skip the "application" part, and go straight to Ch. 10
There are detailed notes available for this lecture.
Gas. Ch. 10

Lecture 31:
Wed, Nov 5, 1997
Exam review/questions + Brief discussion of separation of variables.
There are detailed notes available for this lecture.

Lecture 32:
Fri, Nov 7, 1997
1st conclusions regarding separation of variables. Angular momentum and Ylm's.
There are detailed notes available for this lecture.

Lecture 33:
Mon, Nov 10, 1997
Angular momentum, rotational invariance, Noether's theorem..
There are detailed notes available for this lecture.

Lecture 34:
Wed, Nov 12, 1997
Summarize angular momentum/rotational invariance, start radial equation. Infinite (spherical) well.
There are detailed notes available for this lecture.

Lecture 35:
Fri, Nov 14, 1997
Finish infinite (spherical) well, nuclear magic numbers. Introduce finite (spherical) well.
There are detailed notes available for this lecture.

Lecture 36:
Mon, Nov 17, 1997
Finite (spherical) well. Scattering and bound states. (Intro to Ch. 11, Ylm's again)
There are detailed notes available for this lecture.
Gas. Ch. 11

Lecture 37:
Wed, Nov 19, 1997
Figuring out the Ylm's by operator methods. (Raising and lowering operators for m)_
There are detailed notes available for this lecture.

Lecture 38:
Fri, Nov 21, 1997
Continuing with the Ylm's by operator methods. Also, quiz on radial wavefunctions.
There are detailed notes available for this lecture.

Lecture 39:
Mon, Nov 24, 1997
Finish our discusion of the Ylm's, discuss their completeness (and orthonormality). Begin Ch. 12, set up the Hydrogen radial equation.
There are detailed notes available for this lecture.
Gas. Ch. 12

Lecture 40:
Wed, Nov 26, 1997
Solve the Hydrogen radial equation.
There are detailed notes available for this lecture.
(Fri, Nov 28
Thanksgiving Holiday)

Lecture 41:
Mon, Dec 1, 1997
Hydrogen radial wave functions.
There are detailed notes available for this lecture.

Lecture 42:
Wed, Dec 3, 1997
Hydrogen energies and degeneracies, and start Ch. 8 Introduction to N-particle systems.
There are detailed notes available for this lecture.
Gas. Ch. 8

Lecture 43:
Fri, Dec 5, 1997
Quiz (hydrogen) + more on N-particle systems.
There are detailed notes available for this lecture.

Lecture 44:
Mon, Dec 8, 1997
Solving N-particle systems. Intro to "identical particles".
There are detailed notes available for this lecture.

Lecture 45:
Wed, Dec 10, 1997
Final lecture!
There are detailed notes available for this lecture.


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