Fall Term 2006

As easy as 3.14159265358979323846264338327950288419716

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Last class was:
Mon. 4 Dec. 2006
1:25 - 2:15 PM, Rm.306 Nielsen

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Final Exam!
Thu. 14 Dec. 2006
5:00 - 7:00 PM, Rm.306 Nielsen
Open books, open notes. Bring a bluebook.
Also, bring a calculator just in case.

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BBC World Service news summary

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Instructor: Ted Barnes



Text: E. Merzbacher, Quantum Mechanics

or your favorite text of the same title.
The many similar but less expensive possibilities include
Landau and Lifshitz, Messiah (2 vols. in 1, a good deal!), Griffiths (very clear but basic, and expensive)
Schiff (excellent but expensive and out of stock), Dicke and Wittke, ...

Alt. (supplemental) Text: L. Pauling and E. B. Wilson,
Intro. to Quantum Mechanics With Applications to Chemistry.
(Available at Barnes and Noble for an absurdly low price. Also at Amazon.com .)

Also recommended (mainly for 2nd term):
Group Theory and Quantum Mechanics (M.Tinkham)
Angular Momentum in Quantum Mechanics (A.R.Edmonds) and/or
Elementary Theory of Angular Momentum (M.E.Rose)

QM 1 topics
Classical physics in 1900. Atomic stability. Black-body radiation and Planck's quantum hypothesis. Bohr atom, old QM. deBroglie's pilot waves. Schrödinger equation. Expectation values. Heisenberg's uncertainty principle. 1D square well, SHO. The Schrödinger equation in 3D. Central potentials and the quantization of orbital angular momentum. 3D Coulomb and SHO problems. Stationary-state perturbation theory. Variational method. Degenerate perturbation theory. Linear Stark effect. Spin; spins in magnetic fields. Addition of angular momenta; Clebsch-Gordan problem. Irreducible tensors, Wigner-Eckart theorem. Heliumlike atoms. Probability current density. Quadratic Stark effect. Feynman-Hellman theorem.

Class notes (pdf)
Lecture Notes 0 Class organization. Lecture Notes 1 Classical physics ca.1900. CM and EM, relativity; atomic stability; spectral lines; black body radiation, density of states; Planck's hypothesis. Lecture Notes 2 "Old" quantum mechanics, Bohr H atom; de Broglie, pilot waves; Davisson and Germer; free Schrödinger equation, eigenfunctions and eigenvalues; full time-dependent and time-independent Schrödinger equation; Copenhagen interpretation; constant potential; qualitative nature of 1D wavefunctions; 1D infinite square well. Lecture Notes 3 1D infinite square well. Normalization. Heisenberg Uncertainty Principle. Finite depth 1D square well, boundary conditions on psi(x). 1D SHO, ground state and excited states. Expectation values, SHO examples, "sandwich formula." QM Aside 0 Graphical solution of 1D finite square well (even) bound states. (pdf) QM Aside 1 Calculation of SHO matrix elements using explicit wfns. (pdf) QM Aside 2 Creation and annihilation (raising and lowering) operators for the 1D SHO. (pdf) QM Aside 3 Beautiful 1D SHO wfn plots (postscript): psi_0 psi_1 psi_2 psi_3 psi_n, n=0,100 psi_n, n=0,100 (detail) |psi^2| for n=0, 100 |psi^2| for n=100 versus P_classical Lecture Notes 4 3D bound state problems. Schrödinger equation in spherical coordinates. Separation of variables, Legendre functions and spherical harmonics. Radial wavefunction and centrifugal barrier. Angular momentum operators, their eigenvalues and commutation relations. Lecture Notes 5 3D Coulomb and SHO problems. Summary for midterm Pre-midterm summary of topics. Lecture Notes 6 Nondegenerate perturbation theory: general results. QM Aside 4. High order perturbation theory example: 1D SHO with H_I = gx^4. {c_n} E_0(g) coeffs analytically to 33rd order! (also gives their prime factors) plot of |c_n|, log/lin Lecture Notes 7 Variational method. Lecture Notes 8 Degenerate perturbation theory. Stark effect. Lecture Notes 9 Spin, general results. Interaction with magnetic fields. Combining two spin-1/2 states. Lecture Notes 10 General S1xS2 Clebsch-Gordan problem. Gaunt formula Irreducible tensor operators and the Wigner-Eckhart theorem Helium Probability current QM Aside 5. Current densities in hydrogen (png): 2P(m=+1) 3D(m=+2) 3D(m=+1) 2nd order Stark effect

Problem sets and exams
Problem Set 1 | Tex | ps | pdf || Due Wed. 30 Aug. 2006 Problem Set 2 | Tex | ps | pdf || Due Wed. 06 Sep. 2006 Problem Set 3 | Tex | ps | pdf || Due Wed. 13 Sep. 2006 Problem Set 4 | Tex | ps | pdf || Due Wed. 20 Sep. 2006 Problem Set 5 | Tex | ps | pdf || Due Wed. 27 Sep. 2006 Midterm Exam | Tex | ps | pdf | solns(pdf) || 09 Oct. 2006 Problem Set 6 | Tex | ps | pdf || Due Wed. 25 Oct. 2006 Problem Set 7 | Tex | ps | pdf || Due Wed. 01 Nov. 2006 Problem Set 8 | Tex | ps | pdf || Due Wed. 08 Nov. 2006 Problem Set 9 | Tex | ps | pdf || Due Wed. 15 Nov. 2006 Problem Set 10 | Tex | ps | pdf || Due Mon. 27 Nov. 2006 Final Exam | Tex | ps | pdf || solns(pdf)

Reference links
Physical constants (NIST) Abramowitz and Stegun Handbook of Mathematical Functions Clebsch-Gordan coefficients (PDG)

Utilities
Clebsch-o-matic (Paul Stevenson's Java programs for CG and related angular coefficients.) Grace (A publication quality plotting program you should know about.)

Amusements
Max Planck Louis de Broglie Erwin Schrödinger Hermite, Monsieur Charles Legendre, Monsieur Adrien-Marie Laguerre, Monsieur Edmond Nicholas Schrödinger models the latest fashions Stark makes a bad career move Atomic Orbitals Hydrogenic Wavefunctions

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Grading:

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CLASS AUDIO...

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