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- Title: hw4
- Type: Notes
- School: Washington
- Course: PHYS 513
- Term: Fall
Coursehero >> Washington >> Washington >> PHYS 513
Path: Washington >> PHYS >> 514 Fall, 2008
Path: Washington >> PHYS >> 514 Fall, 2008
Path: Washington >> PHYS >> 517 Fall, 2008
Path: Washington >> PHYS >> 518 Fall, 2008
Path: Washington >> PHYS >> 518 Fall, 2008
Path: Washington >> PHYS >> 518 Fall, 2008
Path: Washington >> PHYS >> 519 Fall, 2008
Path: Washington >> PHYS >> 519 Fall, 2008
Path: Washington >> PHYS >> 519 Fall, 2008
Path: Washington >> PHYS >> 519 Fall, 2008
Path: Washington >> PHYS >> 528 Winter, 2008
Path: Washington >> PHYS >> 528 Winter, 2008
Path: Washington >> PHYS >> 528 Winter, 2008
Path: Washington >> PHYS >> 542 Fall, 2008
Path: Washington >> PHYS >> 544 Fall, 2008
Path: Washington >> PHYS >> 544 Fall, 2008
Path: Washington >> PHYS >> 545 Spring, 2008
Path: Washington >> PHYS >> 545 Spring, 2008
Path: Washington >> PHYS >> 554 Fall, 2008
Path: Washington >> PHYS >> 555 Fall, 2008
Path: Washington >> PHYS >> 555 Fall, 2008
Path: Washington >> PHYS >> 555 Fall, 2008
Path: Washington >> PHYS >> 557 Fall, 2008
Path: Washington >> PHYS >> 558 Winter, 2008
Path: Washington >> PHYS >> 558 Winter, 2008
Path: Washington >> PHYS >> 560 Fall, 2008
Path: Washington >> PHYS >> 567 Winter, 2008
Path: Washington >> PHYS >> 567 Winter, 2008
Path: Washington >> PHYS >> 570 Fall, 2008
Path: Washington >> PHYS >> 572 Spring, 2008
Path: Washington >> PHYS >> 576 Fall, 2008
Path: Washington >> PHYS >> 576 Fall, 2008
Path: Washington >> PHYS >> 576 Fall, 2008
Path: Washington >> PHYS >> 576 Fall, 2008
Path: Washington >> PHYS >> 578 Fall, 2008
Path: Washington >> PHYS >> 581 Fall, 2008
Path: Washington >> PHYS >> 581 Fall, 2008
Path: Washington >> PHYS >> 582 Fall, 2008
Path: Washington >> PHYS >> 583 Fall, 2008
Path: Washington >> PHYS >> 587 Fall, 2008
Path: Washington >> EDC&I >> 436 Fall, 2008
Path: Washington >> POL S >> 205 Fall, 2008
Path: Washington >> POL S >> 205 Fall, 2008
Path: Washington >> POL S >> 205 Fall, 2008
Path: Washington >> POL S >> 205 Fall, 2008
Path: Washington >> POL S >> 213 Fall, 2008
Path: Washington >> POL S >> 246 Spring, 2008
Path: Washington >> POL S >> 246 Spring, 2008
Path: Washington >> POL S >> 246 Spring, 2008
Path: Washington >> POL S >> 249 Winter, 2008
Path: Washington >> POL S >> 249 Winter, 2008
Path: Washington >> POL S >> 249 Winter, 2008
Path: Washington >> POL S >> 249 Winter, 2008
Path: Washington >> POL S >> 270 Spring, 2008
Path: Washington >> POL S >> 270 Spring, 2008
Path: Washington >> POL S >> 270 Spring, 2008
Path: Washington >> POL S >> 270 Spring, 2008
Path: Washington >> POL S >> 273 Fall, 2008
Path: Washington >> POL S >> 273 Fall, 2008
Path: Washington >> POL S >> 273 Fall, 2008
Path: Washington >> POL S >> 273 Fall, 2008
Path: Washington >> POL S >> 281 Winter, 2008
Path: Washington >> POL S >> 281 Winter, 2008
Path: Washington >> POL S >> 281 Winter, 2008
Path: Washington >> POL S >> 281 Winter, 2008
Path: Washington >> POL S >> 299 Winter, 2008
Path: Washington >> POL S >> 299 Winter, 2008
Path: Washington >> POL S >> 299 Winter, 2008
Path: Washington >> POL S >> 299 Winter, 2008
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513 Physics Homework Set #4 Due in class 10/23/08 300 pts Autumn 2008 1. (100 pts) Consider a system composed of two conducting spheres of radius a1 and a2 separated by a distance d with d >> ai . a. (50 pts) Show tha the capacitance matrix for this system is C = d2 d2 4 0 a 1 a2 a a1d 2 a1 a a1d 2 a2 b. (25 pts) If the sphere of radius a1 carries charge Q1 and the sphere of radius a2 carries charge Q2 , what is the energy of the electric eld? c. (25 pts) By placing charge +Q on one sphere and charge Q on the other, what is the capacitance of the system as convetionally de ned? (x) 2. (60 pts) Prove 0 dx sinx2 = , by converting the integral to a contour 2 integral which can be evaluated by suitably closing contours. 2 3. (60 pts) Evaluate (by converting to a contour integral) I(k, a) = dxeikx /(x2 + a2 ) for real values of k. The number a may be complex (provided it is not pure imaginary). Assume, without loss of generality, that (a) > 0. 4. (80 pts) Find the solution, two di erent ways, to the one-dimensional Green d2 s function de ned by dx2 + 2 G(x, x ) = (x x ), with boundary conditions that G(x, x ) remain bounded as x or x go to . is real (this would be electrostatics in a world with a massive photon). d a. (20 pts) Write down eigenfunctions of the lienar operator dx2 + 2 satisfying the boundary conditions, and express G(x, x ) as a linear combination (i.e., and integral) of these eigenfunctions. 2 b. (30 pts) Solve the di erential equation directly by writing down the most general homogeneous solution for x < x which obeys the boundary condition as x , writing down the most general homogeneous solution for x < x which obeys the boundary condition as x + , enforcing continuity at x = x d and requiring that the rst derivative dx G(x, x ) be discontinuous by the correct 2 d amount so that dx2 + 2 acting on G produces the right delta function. c. (30 pts) Perform the integral in your result for part (a) and verify that this agrees with (b) [Hint: Have you done problem 3 already?] 1
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Path: Washington >> PHYS >> 513 Fall, 2008
Description: Physics 513 Homework Set #1 Due in class 10/2/08 300 pts Autumn 2008 1. (100 pts) Consider an (unrealistic) classical model of an electron in which all the charge of the electron resides on a shell of radius r1 and uniform surface charge density (...
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Description: A 9 9 Q X7 X Qb7 9V f Q vI f V fb f n iVb X X Q Ey7U8pWbWTt@a8pE2c88URlwUp3pWbuchx \" 8c ( EpUCYpWbUhs\"8t7 b7 fb nQ f ` Ai 9 x XQb W9cpRYphh1R8tYq8\"p@mh@pktpYhun } mzr ( 8pEc@8pcY@tUg%h vViiVI q V iI Qb7IV q Q VI7 v 97 VIV f IQb...
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Description: Physics 519: HW3 (due in class Wed. April 23, 2008) First some exercises, i.e. straightforward calculations that you should do at least once. These do not, however, need to be turned in. Consider scattering by a central potential with range R (so V ...
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Description: Physics 519: HW7 (due in class FRIDAY May 30, 2008) First some exercises, i.e. straightforward calculations that you should do at least once. These do not, however, need to be turned in. Writing the total number operator in terms of and . Show th...
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Description: Physics 519: HW1 (due in class Wed. April 9, 2008) First some exercises, i.e. straightforward calculations that you should do at least once. These do not, however, need to be turned in. Show that the permutation operator P12 is hermitian. Now the pr...
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gamma0-246-2-14.txtPath: Washington >> POL S >> 246 Spring, 2008
Description: (246, 2, 14) (0.59603700000002391, 0.0039999999999054126, 0.0, 0.0, 0.60003699999992932) Modular Symbols space of dimension 0 and level 246, weight 2, character [1, -1, zeta4], sign 1, over Cyclotomic Field of order 4 and degree 2 ...
Poster_Get Moving Be Active DOH 961-246.pdfPath: Washington >> POL S >> 246 Spring, 2008
Description: Active Families: Play Together Walk Together Grow Together Take one step at a time oving! Be Active! tM e G Get Moving! Be Active! DOH Pub 961-246 (Rev. 3/05) Illustrations reproduced from Bright Futures in Practice: Physical Activity with pe...
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Description: CREDIT CONTAGION AND AGGREGATE LOSSES Kay Giesecke Cornell University Stefan Weber TU Berlin October 26, 2002 Abstract Credit contagion refers to the propagation of economic distress from one rm or sovereign government to another. In this paper we ...
249-W09 TA Job Description-Levi.pdfPath: Washington >> POL S >> 249 Winter, 2008
Description: Political Science Department Winter 2009 Teaching Assistant Job Description Complete and return to Meera Roy by XXX *COMPLETE THIS TOP SECTION AND SIGN BELOW* TA NAME: _ QUIZ MEETINGS: Sections (AA, etc) Days Times Locations 1. _ 2. _ TA OFFICE LO...
Poster_Your kids learn to be active from you DOH 961-249.pdfPath: Washington >> POL S >> 249 Winter, 2008
Description: oving! Be Active! tM e G Your Kids Learn To Be Active From YOU! Families say: I try to be a good role model for my kids. Sometimes we just put music on and dance around in the living room. He was having trouble riding his bike, so I just got on and ...
POL S_HIST 249 WIN_05 long.pdfPath: Washington >> POL S >> 249 Winter, 2008
Description: winter 2005 POL S/HIST/SOC 249/266 any Jacoby Site: Committee for General Amnesty and Social Justice Seattle WA 98102 URL www.comiteproamnistia.org Address: PO Box 12252 Location: 150 Denny Way Seattle WA 98109 Overview: The Comit Pro-Amnista...
POL S 249-HIST-SOC 266 long.pdfPath: Washington >> POL S >> 249 Winter, 2008
Description: Service Learning Organizations and Positions winter 2006 POL S/HIST/SOC 249/266 any Levi Site: Location: Community Coalition for Environmental Justice Seattle WA 98122 URL www.ccej.org Address: 2820 East Cherry St. Overview: Mission: Our mission ...
270 S07 Assignment 1b Grading.pdfPath: Washington >> POL S >> 270 Spring, 2008
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gamma0-273-2-28.txtPath: Washington >> POL S >> 273 Fall, 2008
Description: (273, 2, 28) (0.52403199999935168, 0.016000999999960186, 0.0, 0.0, 0.54003299999931187) Modular Symbols space of dimension 0 and level 273, weight 2, character [1, -zeta6 + 1, zeta6], sign 1, over Cyclotomic Field of order 6 and degree 2 ...
273-1.pdfPath: Washington >> POL S >> 273 Fall, 2008
Description: What is Required for a Student to be Successful in this Course: The assignments and readings are from a previous Quarter listed. They are subject to change use as an example ONLY. Class Participation Types of Assignments Two on site sessions. One we...
gamma0-273-2-5.txtPath: Washington >> POL S >> 273 Fall, 2008
Description: (273, 2, 5) (0.084006000000044878, 0.12000799999987066, 0.83605199999965407, 0.25201500000002852, 1.2920809999995981) Modular Symbols space of dimension 40 and level 273, weight 2, character [1, 1, -1], sign 1, over Rational Field ...
gamma0-273-2-38.txtPath: Washington >> POL S >> 273 Fall, 2008
Description: (273, 2, 38) (2.3481459999993604, 2.5841620000001058, 0.0, 40.994562000000769, 45.926870000000235) Modular Symbols space of dimension 37 and level 273, weight 2, character [-1, zeta6, zeta6], sign 1, over Cyclotomic Field of order 6 and degree 2 ...
ENGL 281 W_04 Sites and Positions.pdfPath: Washington >> POL S >> 281 Winter, 2008
Description: Service Learning Sites and Positions ENGL Site: 281 C Suite 203 winter Seattle URL 2004 Simmons-O\'Neill WA 981042959 Chinese Information and Service Center Address: 409 Maynard Ave. S. Location: Bush Hotel, Chinatown (main office) Youth progra...
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Description: POTENTIAL IMPLICATIONS OF PCM CLIMATE CHANGE SCENARIOS FOR SACRAMENTOSAN JOAQUIN RIVER BASIN HYDROLOGY AND WATER RESOURCES NATHAN T. VANRHEENEN, ANDREW W. WOOD, RICHARD N. PALMER and DENNIS P. LETTENMAIER Department of Civil and Environmental Enginee...
281.pdfPath: Washington >> POL S >> 281 Winter, 2008
Description: Goodness-of-t of the Heston model Gilles Daniel1 1 2 David S. Br e1 e Nathan L. Joseph2 Computer Science Department Manchester School of Accounting & Finance University of Manchester, U.K. gilles.daniel@cs.man.ac.uk http:/www.cs.man.ac.uk/danielg ...
gamma0-281-2-2.txtPath: Washington >> POL S >> 281 Winter, 2008
Description: (281, 2, 2) (2.08813, 11.056690999999999, 0.0, 103.502469, 116.65128999999999) Modular Symbols space of dimension 25 and level 281, weight 2, character [zeta140], sign 1, over Cyclotomic Field of order 140 and degree 48 ...
gamma0-299-2-1.txtPath: Washington >> POL S >> 299 Winter, 2008
Description: (299, 2, 1) (0.49603100000058475, 0.0039999999999054126, 0.0, 0.0, 0.50003100000049017) Modular Symbols space of dimension 0 and level 299, weight 2, character [1, zeta22], sign 1, over Cyclotomic Field of order 22 and degree 10 ...
gamma0-299-2-7.txtPath: Washington >> POL S >> 299 Winter, 2008
Description: (299, 2, 7) (1.4440910000002987, 1.3040810000002239, 0.0, 53.19932499999959, 55.947497000000112) Modular Symbols space of dimension 28 and level 299, weight 2, character [zeta12, -1], sign 1, over Cyclotomic Field of order 12 and degree 4 ...
gamma0-299-2-3.txtPath: Washington >> POL S >> 299 Winter, 2008
Description: (299, 2, 3) (0.05200299999978597, 0.0039999999999054126, 0.0, 0.0, 0.056002999999691383) Modular Symbols space of dimension 0 and level 299, weight 2, character [1, -1], sign 1, over Rational Field ...
gamma0-299-2-13.txtPath: Washington >> POL S >> 299 Winter, 2008
Description: (299, 2, 13) (1.6201019999998607, 11.752733999999691, 0.0, 31.413963000000876, 44.786799000000428) Modular Symbols space of dimension 28 and level 299, weight 2, character [zeta44^11, zeta44^2], sign 1, over Cyclotomic Field of order 44 and degree 20...