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Cornell - P - 651
Cornell University Department of Physics Phys 651 November 22, 2006Relativistic Quantum Field Theory, Fall 2006 Homework Assignment # 12(Due Wednesday, November 29, after the lecture.) Lectures and Reading Assignments: Readings are from An Introdu
Cornell - P - 443
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Cornell - P - 443
Physics 443M. Neubert, S.J. LeeCourse OrganizationSpring 2006Lectures and Section Lectures are 9:059:55 am on Monday, Wednesday and Friday in 110 Rockefeller. Section meetings are 3:354:25 pm on Friday in 231 Rockefeller. The instructor of the
Cornell - P - 443
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Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 1M. Neubert, S.J. Lee(due February 1)Spring 20061. The relation between frequency and wave length in a cavity is () = c2 2 - 0,0 = const.Using that = 2 and k = 2/, find the dispersion relation (k). What are the
Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 2M. Neubert, S.J. Lee(due February 8)Spring 20061. Solve the time-independent Schrdinger equation for a centered infinite square well o with an attractive -function potential in the center: V (x) = -c (x) ; if -a < x <
Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 3M. Neubert, S.J. Lee(due February 15)Spring 20061. Find expressions for the operators p and x in the momentum representation. For ^ ^ an arbitrary state in Hilbert space, evaluate the brackets p|^| and |^| in x x term
Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 4M. Neubert, S.J. Lee(due February 22)Spring 20061. a) For the one-dimensional harmonic oscillator, show that a coherent state of the form | N exp(^+ )|0 awith arbitrary complex (and N a normalization factor) is an
Cornell - P - 443
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Cornell - P - 443
Physics 443 Preliminary Exam 1M. Neubert, S.J. Lee(February 23)Spring 20061. Write down the time-dependent Schrdinger equation for a free particle in the o momentum representation, where the wave function is (p, t) = p|(t) . Solve this equatio
Cornell - P - 443
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Cornell - P - 443
Physics 443 Preliminary Exam 1 SolutionsM. Neubert, S.J. Lee(February 23)Spring 20061. Write down the time-dependent Schrdinger equation for a free particle in the o momentum representation, where the wave function is (p, t) = p|(t) . Solve t
Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 5M. Neubert, S.J. Lee(due March 1)Spring 20061. The eigenfunctions of the hydrogen atom corresponding to maximal angular momentum (l = n - 1) are n,n-1,m (r, , ) = 1 (2n)! 2 na3 22r nan-1m e-r/na Yn-1 (, ) ,whe
Cornell - P - 443
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Cornell - P - 443
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Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 7M. Neubert, S.J. Lee(due March 15)Spring 20061 1. For a particle with spin 2 , construct the matrix n S representing the component of spin along a direction n parameterized in terms of spherical coordinates,sin cos
Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 8M. Neubert, S.J. Lee(due March 29)Spring 20061. A system consisting of two particles with spins s1 and s2 is governed by the potential V = V1 (r) + V2 (r) s1 s2 + V3 (r) L S , where r = |r 1 - r2 |, L is the orbital
Cornell - P - 443
Physics 443 Problem Set 9M. Neubert, S.J. Lee(due April 5)Spring 20061. The ClebschGordan coefficients for the addition of orbital angular momentum 1 l = 0 and spin s = 2 to total spin j = l 1 can be written as 21 1 |jmj = A |l(mj - 2 ) | 2
Cornell - P - 443
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Cornell - P - 443
Physics 443 Problem Set 10M. Neubert, S.J. Lee(due April 12)Spring 20061. The fundamental problem in harnessing nuclear fusion is getting two nuclei close enough together for the attractive (but short-range) nuclear force to overcome the Coulo
Cornell - P - 443
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Cornell - P - 443
Physics 443 Preliminary Exam 2M. Neubert, S.J. Lee(April 4)Spring 20061. The Hamiltonian for a particle of charge q in an electro-magnetic field is H= 1 (p - qA(r, t)2 + q (r, t) . 2mThe scalar and vector potentials, and A, determine the el
Cornell - P - 443
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Cornell - P - 443
Physics 443 Preliminary Exam 2 SolutionsM. Neubert, S.J. Lee(April 4)Spring 20061. The Hamiltonian for a particle of charge q in an electro-magnetic field is H= 1 (p - qA(r, t)2 + q (r, t) . 2mThe scalar and vector potentials, and A, deter
Cornell - P - 443
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Cornell - P - 443
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Cornell - P - 443
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Cornell - P - 443
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Cornell - P - 651
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Cornell - P - 651
Relativistic Quantum Field Theory(Physics 651)Mon & Wed: 8:40 am 9:55 am Rockefeller 112This course will provide a modern introduction to relativistic quantum field theory - a subject most working physicists need to know about. The course is int
Cornell - P - 651
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Cornell - P - 651
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Berkeley - EE - 232
EE 232 Lightwave Devices Lecture 13: Rate Equations and Dynamic Response of Semiconductor LasersReading: Chuang, Sec. 11.1 11 2 Chuang Sec 11 1 11.2 (See also Coldren, Sec. 5.1 5.3) (The Notes follow primarily Coldrens book) Instructor: Ming C. Wu
Berkeley - EE - 232
EE 232 Lightwave Devices Lecture 17: Polarization DependenceReading: Chuang, Sec. 4.1-4.2, 9 5 Chuang Sec 4 1 4 2 9.5 (There is also a good discussion in Coldren, Appendix 8 and 10) Instructor: Ming C. Wu University of California, Berkeley Electrica
Berkeley - EE - 232
EE 232 Lightwave Devices Lecture 21: Light-Emitting Diode (LED)Instructor: Ming C. Wu University of California, Berkeley Electrical Engineering and Computer Sciences Dept Dept.EE232 Lecture 21-12008. University of CaliforniaSpontaneous Emissi
Cornell - HMWK - 661
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Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Superstring Theory Fall 2004 Lecture contents (last updated 11/01/04) : 08/26 Introduction to the bosonic string theory.08/31 First quantization of the bosonic string and the appearance of the critical spacetime dimension D = 26 and the gravit
Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 1 Due Tuesday 9/7/04 Read Polchinski Ch 1.8/26/04Read Johnson Ch. 1 and earlier parts of Ch. 2. Part 1 (1) Problem 1.2 (2) For the lightest spin-2 closed string mode to be massless, what is the spacetime dimension and what is the
Cornell - HMWK - 661
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Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 3 Due Tuesday 9/21/0409/09/04Read Chapter 2. Homework problems in this chapter will be given in the next homework set. The Jacobi Theta functions i (z, ) are a canonical set of natural analytic functions of the torus. Here we are
Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 4 Due Tuesday 9/28/04 Finish reading Chapter 2. Part 1 (1) Problem 2.109/16/04Show this result by starting with the standard 2-dimensional Poisson equation. Find the Coulomb potential. Verify Coulomb's law. Now write the Poisson e
Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 5 Due Tuesday 10/05/0409/23/04Briey read Chapter 3. A careful reading of this chapter is reserved for Part II. Part 1 (1) Look at Eq.(3.5.6) (forget about c here). Consider a closed string N-point M-loop scattering amplitude. What
Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 6 Due Tuesday 10/19/04 Read Chapter 8. Part 1 (1) Do Problems 1.5 to 1.9. Part 2:10/07/04(2) Bosonize the bc ghost system and verify the background charge (i.e., the coefficient of the second derivative term in T (z) in the linear
Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 7 Due Tuesday 10/26/04 Finish reading Chapter 8. Part 110/14/04(1) In class, we constructed the T 2 /Z2 orbifold. For a torus with a Z3 symmetry, we find that T 2 /Z2 is a tetrahedron, with the topology of a sphere. What is the sh
Cornell - HMWK - 661
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Cornell - HMWK - 661
P661 Homework # 8 Due Tuesday 11/2/0410/21/04Read Chapter 10 up to p.37. Type I theory will be saved for later. Part 1 (1) Try to understand the content of the 3 tables. (2) If you are not familiar with SO(N ) representations, you may want to con
Cornell - HMWK - 661
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