Quantum Mechanics I, Physics 3220

Class summary

Lectures

Brief summary of lectures

Gas. Ch. 1

Lecture 1:
Mon, Aug 26, 1996 		Introduction, discussion of syllabus. What is quantum mechanics (vs. what is classical mechanics?) Breakdown of classical physics, Blackbody radiation.

Lecture 2:
Wed, Aug 28, 1996 		Limits of Classical Physics: Review of Blackbody radiation, Planck's resolution of the UV catastrophe. Photelectric effect, Compton scattering

Lecture 3:
Fri, Aug 30, 1996 		The old quantum theory Two slit experiment, and the first ideas of wave/particle duality. De Broglie's hypothesis. Bohr model. Intro to wave packets.
Gas. Ch. 2

Lecture 4:
Wed, Sep 4, 1996 		Wave Packets, and Fourier Transforms. Gaussians.
(See Gas Appendix A)

Lecture 5:
Fri, Sep 6, 1996 		(Review of) time evolution of Gaussian packet. Discussion of spreading of this packet with time. Heisenberg uncertainty principle. "Derivation" of Schrodinger Eq'n from our Gaussian packets
Gas. Ch. 3

Lecture 6:
Mon, Sep 9, 1996 		Uncertainty principle discussion. Born's probability interpretation. Consequences of Schrodinger Eqn - linearity, superposition, phases.
(See also Griffiths Ch. 1)

Lecture 7:
Wed, Sep 11, 1996 		Conservation of probability. Probility current, or flux. Momentum as an operator. Introduction to "momentum space".

Lecture 8:
Fri, Sep 13, 1996 		Expectation value of momentum. "Derivation" of the momentum operator. Introduction of momentum space wave function.
Gas. Ch. 4

Lecture 9:
Mon, Sep 16, 1996 		Operators and commutators. Hermiticity - physical operators (observables) have real expectation values. Definitions of eigenvalues, eigenfunctions.
Example: momentum eigenfunctions. Separation of S.E. into time and space - solution of time dependent part. Reduction of TDSE to TISE, which is really an eigenvalue problem.
Puzzle: What "functions" satisfy the eigenvalue problem x_op f(x) = lambda f(x) ?.

Lecture 10:
Wed, Sep 18, 1996 		Mathematics of Dirac delta functions. Solution of T.D.S.E. in one-dimensional infinite well. Discussion of general features of these eigenfunctions.
(See Gas appendix on Delta's)

Lecture 11:
Fri, Sep 20, 1996 		(Quiz) Discussion of quiz - interpretation of flux, and probability distributions in x space and p space. Expansion postulate - Fourier's trick, expanding an arbitrary wave function in a box in energy eigenfunctions of the box. Interpretation of Fourier coefficients.

Lecture 12:
Mon, Sep 23, 1996 		Expansion postulate. How to find the probability of measuring some value of energy when your state is a superposition of eigenfunctions.

Lecture 13:
Wed, Sep 25, 1996 		More expansion postulate: how to expand in other eigenfunctions. Distinction between continuous and discrete eigenvalues.
Gas. Ch. 5

Lecture 14:
Fri, Sep 27, 1996 		Parity, parity eigenfunctions. 1 dimensional problems. Begin with E>0, free particles. discussion of initial conditions (wave packets, flux). Solution of step potential, up or down.

Lecture 15:
Mon, Sep 30, 1996 		More scattering problems. Solving scattering (R and T) off of a "dip" and a "bump". Tunneling.

Lecture 16:
Wed, Oct 2, 1996 		(Review/questions for exam). Tunneling - Gamow's alpha decay calculation.
(Exam I, Th Oct 3, Gas Ch 1-4)

Lecture 17:
Fri, Oct 4, 1996 		Bound states in general. Particle in finite box - even and odd solutions. Graphical solutions for eigenvalues.

Lecture 18:
Mon, Oct 7, 1996 		Delta function potential. Bound states, full solution. Scattering states, R and T. Double delta function - intro.

Lecture 19:
Wed, Oct 9, 1996 		Double delta function - energy levels, time dependence. Harmonic oscillator, introduction and "setup"
Gas. Ch. 6

Lecture 20:
Fri, Oct 11, 1996 		Harmonic oscillator, complete solution (sketched). Abstract idea of wave function, analogy with "abstract vectors" as versus the components of a vector in some coordinate system. Vector basis, expansion, inner product, completeness.

Lecture 21:
Mon, Oct 14, 1996 		More analogies of vector space with function space. Introduction of Dirac's "braket" notation, including separating out the "bra" and "ket" independently. Introduction of operators into braket notation, and operator definition of Hermitian adjoint.

Lecture 22:
Wed, Oct 16, 1996 		More Dirac notation, definition of Hermitian operators. Matrix review, connection of operators with matrices.

Lecture 23:
Fri, Oct 18, 1996 		(Kinney substitutes) Quiz on 1-D potentials.

Lecture 24:
Mon, Oct 21, 1996 		More on Hermitian operators. (4 important theorems!) The postulates of Quantum Mechanics.

Lecture 25:
Wed, Oct 23, 1996 		Simultaneous eigenvalues and compatible observables. (Connection to the commutator) Degeneracy.

Lecture 26:
Fri, Oct 25, 1996 		Generalized uncertainty principle, time evolution of operators.
Gas. Ch. 7

Lecture 27:
Mon, Oct 28, 1996 		Operator methods - solution of the harmonic oscillator.

Lecture 28:
Wed, Oct 30, 1996 		Conclusion of harmonic oscillator. Time dependence of operators.
Gas. Ch. 8

Lecture 29:
Fri, Nov 1, 1996 		Introduction to N body quantum mechanics.

Lecture 30:
Mon, Nov 4, 1996 		Solving the 2-particle problem for free particles, two ways. (Using x1 and x2, or changing variables to relative and center of mass coordinates)

Lecture 31:
Wed, Nov 6, 1996 		Review for exam (questions).
(Exam II, Th Nov 7, Gas Ch 5-7)

Lecture 32:
Fri, Nov 8, 1996 		(Went over test, esp. problem 3) Intro to identical particles. Symmetry, and the exchange operator P12.

Lecture 33:
Mon, Nov 11, 1996 		Pauli exclusion, and (anti)symmetrizing wave functions.
Gas. Ch. 10

Lecture 34:
Wed, Nov 13, 1996 		Brief summary of Ch. 9 (which we skip, at least for now). 3-D Schrodinger equation, reduction of 2-body potentials (in 3-D) to center of mass and relative coordinates. Separation of variables, radial and angular equations.

Lecture 35:
Fri, Nov 15, 1996 		Solution of angular equation, (Y_lm's)

Lecture 36:
Mon, Nov 18, 1996 		First discussion of conservation of angular momentum, and the connection with spherical symmetry. (Classical and quantum) Commutation relations involving angular momentum.

Lecture 37:
Wed, Nov 20, 1996 		Connection of angular momentum with separation of variables. Introduction to the Radial equation. Solution for infinite spherical potential well. (Spherical Bessel functions)

Lecture 38:
Fri, Nov 22, 1996 		Quiz on identical particles. More about Spherical Bessel functions.

Lecture 39:
Mon, Nov 25, 1996 		Radial Equation: Finish Square well: Phase shifts.
Gas. Ch. 11

Lecture 40:
Wed, Nov 27, 1996 		Finish Radial Eqn. Start Ch. 11: Angular Momentum. (Introduction to the "raising and lowering" operators for Lz.)
Thanksgiving holiday

Lecture 41:
Mon, Dec 2, 1996 		More on raising and lowering - derivation of the eigenvalues of L^2 and Lz, and the eigenfunctions, using L+ and L- and the various commutation relations. (General solution for Ylm's)

Lecture 42:
Wed, Dec 4, 1996 		Finish Ch. 11: last few comments about angular momentum, and discussion of "expansion postulate" for Ylm's. (Also FCQ's)
Gas. Ch. 12

Lecture 43:
Fri, Dec 6, 1996 		Start Ch. 12, Hydrogen atom. (Quiz delayed till monday) Set up and (essentially) solve the radial equation. Quantization condition.

Lecture 44:
Mon, Dec 9, 1996 		More on hydrogen atom. Discussion of wave functions, qualitative aspects. Degeneracies. (Short quiz and discussion).

Lecture 45:
Wed, Dec 11, 1996 		Last class! Finish up hydrogen atom. Review for final.

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