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Robert W. Field
CohenTannoudji, 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.

Homework (weekly): 40% (~ten problem sets)

One Exam: 40% (openbook, take home)

InClass Quizzes: 20% (approximately 30)
Tentative Exam Handin 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) timeindependent problems. We will begin with onedimensional problems, treated in the Schrödinger Ψ(x) wavefunction picture. Then Dirac's braket 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 3D 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 WignerEckart theorem, and 3j (ClebschGordan) coefficients. Finally, we deal with manybody systems, exemplified by manyelectron 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. CohenTannoudji, 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 inclass 5minute quizzes, and one takehome, openbook exam. A key difference between problems and the exam is that outofclass 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 inclass quizzes (20%). The quizzes are intended to exercise important concepts or techniques immediately after they are introduced.
Calendar
This calendar provides the lecture topics for the course.

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 



RydbergKleinRees: V(x) from EvJ 


9 



NumerovCooley 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. QuasiDegeneracy. Polyads. 


18 



Variational Method 


19 



Density Matrices I. Initial NonEigenstate Preparation, Evolution, Detection. 


20 



Density Matrices II. Quantum Beats. Subsystems and Partial Traces. 


III. Central Forces and Angular Momentum 


21 



3D Central Force I. Separation of Radial and Angular Momenta. 


22 



3D Central Force II. LeviCivita. ε_{ijk.} 


23 



Angular Momentum Matrix Elements from Commutation Rules 


24 



JMatrices 


25 



H^{SO} + H^{Zeeman}: Coupled vs. Uncoupled Basis Sets 


26 



JLSMJ>↔ LMLMS> by Ladders Plus Orthogonality 


27 



WignerEckart Theorem 


28 



Hydrogen Radial Wavefunctions 


29 



Pseudo OneElectron Atoms: Quantum Defect Theory 


IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice 


30 



Matrix Elements of ManyElectron Wavefunctions 


31 



Matrix Elements of OneElectron, F (i), and TwoElectron, G (i,j) Operators 


32 



Configurations and LSJ "Terms" (States) 


33 



ManyElectron LSJ Wavefunctions: L^{2} and S^{2} Matrices and Projection Operators 


34 



e^{2}/rij and Slater Sum Rule Method 


35 



Spin Orbit: ζ(N,L,S)↔ζnl 


36 



Holes. Hund's Third Rule. Landé gFactor via WE Theorem. 


37 



Infinite 1D Lattice I 


38 



Infinite 1D Lattice II. Band Structure. Effective Mass. 


39 



Catchup 


40 



Wrapup 