Robert W. Field

Cohen-Tannoudji, Diu, and Laloë. Quantum Mechanics. Vols. 1 and 2.

Merzbacher. Quantum Mechanics.
Tinkham. Group Theory and Quantum Mechanics.
Golding. Applied Wave Mechanics.
Condon, and Shortley. The Theory of Atomic Spectra.
Karplus, and Porter. Atoms and Molecules.

Three sessions / week
1 hour / session

One session / week
1 hour / session

• Homework (weekly): 40% (~ten problem sets)
• One Exam: 40% (open-book, take home)
• In-Class Quizzes: 20% (approximately 30)

Tentative Exam Hand-in Date: Lecture 40

This is a course for users rather than admirers of Quantum Mechanics. It will wind its way,with a minimum of elegance and philosophical correctness, through a progression of increasingly complex (mostly) time-independent problems. We will begin with one-dimensional problems, treated in the Schrödinger Ψ(x) wavefunction picture. Then Dirac's bra-ket notation will be introduced and we will switch permanently to Heisenberg's matrix mechanics picture. In matrix mechanics all information resides in a collection of numbers called "matrix elements" and all sorts of trickery will be developed to find ways of deriving the values of all matrix elements without ever actually evaluating any integrals! One can never underestimate the importance of Perturbation Theory. Armed with matrices, we will turn to 3-D central force (spherical symmetry) problems, and discover that for all spherical systems (atoms), the angular factors of all matrix elements are trivially evaluable without approximation. Key topics are commutation rule definitions of scalar, vector, and spherical tensor operators, the Wigner-Eckart theorem, and 3-j (Clebsch-Gordan) coefficients. Finally, we deal with many-body systems, exemplified by many-electron atoms ("electronic structure"), anharmonically coupled harmonic oscillators ("Intramolecular Vibrational Redistribution: IVR"), and periodic solids.

The text is Quantum Mechanics, Volumes 1 and 2, by C. Cohen-Tannoudji, B. Diu, and F. Laloë (CTDL). The point of view of the text is quite different from the lectures (the text is more elegant, analytical, and logical). Reading assignments are intended to complement the lectures. Most homework, but few exam problems, will be based on the CTDL text. Additional reading material will be handed out in class, much of which is notes prepared almost 50 years ago by Professor Dudley Herschbach of Harvard University (while he was an Assistant Professor at Berkeley).

There will be approximately ten weekly problem sets, ~30 in-class 5-minute quizzes, and one take-home, open-book exam. A key difference between problems and the exam is that out-of-class discussion of the problems, but not of the exam, is expected. Problem sets should be handed in at the start of class on the specified due date and will be graded. Course grades will be determined by the average of the ten problem set grades (40%), the exam (40%) and approximately 30 in-class quizzes (20%). The quizzes are intended to exercise important concepts or techniques immediately after they are introduced.

Calendar

 

	LEC #				TOPICS
	I. One Dimensional Problems
	1				Course Outline. Free Particle. Motion?
	2				Infinite Box, δ(x) Well, δ(x) Barrier
	3				|Ψ(x,t)|2: Motion, Position, Spreading, Gaussian Wavepacket
	4				Information Encoded in Ψ(x,t). Stationary Phase.
	5				Continuum Normalization
	6				Linear V(x). JWKB Approximation and Quantization.
	7				JWKB Quantization Condition
	8				Rydberg-Klein-Rees: V(x) from EvJ
	9				Numerov-Cooley Method
	II. Matrix Mechanics
	10				Matrix Mechanics
	11				Eigenvalues and Eigenvectors. DVR Method.
	12				Matrix Solution of Harmonic Oscillator (Ryan Thom Lectures)
	13				Creation (a† ) and Annihilation (a) Operators
	14				Perturbation Theory I. Begin Cubic Anharmonic Perturbation.
	15				Perturbation Theory II. Cubic and Morse Oscillators.
	16				Perturbation Theory III. Transition Probability. Wavepacket. Degeneracy.
	17				Perturbation Theory IV. Recurrences. Dephasing. Quasi-Degeneracy. Polyads.
	18				Variational Method
	19				Density Matrices I. Initial Non-Eigenstate Preparation, Evolution, Detection.
	20				Density Matrices II. Quantum Beats. Subsystems and Partial Traces.
	III. Central Forces and Angular Momentum
	21				3-D Central Force I. Separation of Radial and Angular Momenta.
	22				3-D Central Force II. Levi-Civita. εijk.
	23				Angular Momentum Matrix Elements from Commutation Rules
	24				J-Matrices
	25				HSO + HZeeman: Coupled vs. Uncoupled Basis Sets
	26				|JLSMJ>↔ |LMLMS> by Ladders Plus Orthogonality
	27				Wigner-Eckart Theorem
	28				Hydrogen Radial Wavefunctions
	29				Pseudo One-Electron Atoms: Quantum Defect Theory
	IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice
	30				Matrix Elements of Many-Electron Wavefunctions
	31				Matrix Elements of One-Electron, F (i), and Two-Electron, G (i,j) Operators
	32				Configurations and L-S-J "Terms" (States)
	33				Many-Electron L-S-J Wavefunctions: L2 and S2 Matrices and Projection Operators
	34				e2/rij and Slater Sum Rule Method
	35				Spin Orbit: ζ(N,L,S)↔ζnl
	36				Holes. Hund's Third Rule. Landé g-Factor via W-E Theorem.
	37				Infinite 1-D Lattice I
	38				Infinite 1-D Lattice II. Band Structure. Effective Mass.
	39				Catch-up
	40				Wrap-up