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Exam Study Guide - Classical Physics - Fall 2009 | Physics 7, Exams of Physics

University of California - IrvinePhysics

Material Type: Exam; Class: CLASSICAL PHYSICS; Subject: Physics; University: University of California - Irvine; Term: Winter 2009;

Typology: Exams

Pre 2010

Uploaded on 09/17/2009

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P113C Schedule
Winter, 2009
Module 1 Time-dependent perturbation theory, the two- and three-level systems (Gri 9,
Gas 15, 18.3, 18.4, Gas Suppl 15-A, 18-B), interactions of charged particles with the
electromagnetic field (Gas 16), NMR, atomic and nuclear radiation, photoelectric effect,
photodisintegration (Gas 17). (about 3 weeks)
Module 2 Adiabatic and Sudden approximations (Gri 10, Gas Suppl 16-A) (about a
week)
Module 3 Scattering (Gri 11, Gas 19) (about 2 weeks)
Module 4 Relativistic QM: Relativistic free electron theory Griffths Particle Physics 7,
Gingrich notes (online), Relativistic treatment of H atom (Moss Ch 11, Zopyros notes
online), Into to QED (Gas Suppl 18-A, online references) (about 3 weeks)
Midterm Exam 2/5
This schedule is flexible and subject to change as we work through the material.
Problems are due on Tuesdays. Be prepared to present solutions during the discussion
section.
Problem Set 1: Griffths 9.1, 9.2, 9.3, 9.4, 9.7, 9.9. I have done some of these in class,
namely 9.1, 9.2, 9.7. However it will be valuable for you to work through those problems
and write out the solutions.
Problem Set 2: Griffths 9.11, 9.14, 9.20, M1 transitions. Again I have done some of these
in class but you should work through them.
Problem on M1 transitions
Work through the derivation of the M1 rate and calculations for transitions
in hydrogen, following my presentation in class.
a. From H' = -\mu \cdot B, derive the expression for A, starting with that for
E1.
b. Obtain the selection rules for n, l and m
c. Compare the magnitudes of E1 and M1 transitions
d.. Show that without spin, there are no M1 transition between
hydrogenic levels
pf3

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P113C Schedule Winter, 2009 Module 1 Time-dependent perturbation theory, the two- and three-level systems (Gri 9, Gas 15, 18.3, 18.4, Gas Suppl 15-A, 18-B), interactions of charged particles with the electromagnetic field (Gas 16), NMR, atomic and nuclear radiation, photoelectric effect, photodisintegration (Gas 17). (about 3 weeks) Module 2 Adiabatic and Sudden approximations (Gri 10, Gas Suppl 16-A) (about a week) Module 3 Scattering (Gri 11, Gas 19) (about 2 weeks) Module 4 Relativistic QM: Relativistic free electron theory Griffths Particle Physics 7, Gingrich notes (online), Relativistic treatment of H atom (Moss Ch 11, Zopyros notes online), Into to QED (Gas Suppl 18-A, online references) (about 3 weeks) Midterm Exam 2/ This schedule is flexible and subject to change as we work through the material. Problems are due on Tuesdays. Be prepared to present solutions during the discussion section. Problem Set 1: Griffths 9.1, 9.2, 9.3, 9.4, 9.7, 9.9. I have done some of these in class, namely 9.1, 9.2, 9.7. However it will be valuable for you to work through those problems and write out the solutions. Problem Set 2: Griffths 9.11, 9.14, 9.20, M1 transitions. Again I have done some of these in class but you should work through them. Problem on M1 transitions Work through the derivation of the M1 rate and calculations for transitions in hydrogen, following my presentation in class. a. From H' = -\mu \cdot B, derive the expression for A, starting with that for E1. b. Obtain the selection rules for n, l and m c. Compare the magnitudes of E1 and M1 transitions d.. Show that without spin, there are no M1 transition between hydrogenic levels

e. Consider the n=2 fine structure of hydrogen. Write out the Clebsch-Gordon expansion of the j=3/2 m=3/2,1/2 states and the j=1/2 m=1/2, -1/2 states. f. Write out the magnetic moment operator in terms of the L and S operators. g. Calculate A for the transition from (3/2 3/2) to (1/2 1/2). Calculate A for the transitions from (3/2 1/2) to (1/2 1/2) and (1/2 -1/2). Show that the M1 rates from each of initial levels are the same. h. Consider the n=1 hyperfine structure for hydrogen. Write out the Clebsch-Gordon expansion of the S=1 and S=0 states and the magnetic moment operator in terms of S_e and S_p. i. Calculate A for the transition from any of the S=1 states to the S=0 state. Problem Set 3: Gasiorowicz Ch. 17, p. 269 Problems 1, 2, 3 http://www.ps.uci.edu/~markm/eee/47480w08/gasiorowicz_chapter_17.pdf Problem on Einstein Summation Convention Repeat the demonstration from class of A X (B X C) = B (A.C) - C (A .B). Show that (A X B). (C X D) = (A. C)(B. D) - (A. D)(B. C) Show that div (curl A) = 0 and curl (grad P) = 0. In both cases when you write them out using the Einstein convention you see that you are summing over a symmetrical tensor times an antisymmetrical tensor. Show that for A = -1/2 r X B for B a constant vector curl A = B Problem Set 4: Griffths Problem 10.1 (p. 370), Problem 10.2 (p. 376) Problem Set 5:

  1. Calculate the differential cross section for Coulomb scattering of a negative muon from a hydrogen atom in its ground state. Is there any difference for the scattering of a positive muon from?
  2. Calculate the differential cross section for Coulomb excitation of a hydrogen atom from its ground state by a negative muon to a. the 2S state, b. to the 2P state.
  3. Consider the spin-dependent potential V(r) \sigma_{\mu} \cdot \sigma_e. Calculate the differential cross section for scattering of an unpolarized negative muon from an unpolarized hydrogen atom. Griffiths Problems 11.10, 11.13 without the last parts.