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Course: P 443, Fall 2009
School: Cornell
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%%Creator: %!PS-Adobe-2.0 dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: PS2.dvi %%Pages: 2 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMSS17 CMSS12 CMR12 CMMI12 CMEX10 CMSY10 CMMI8 CMR8 %%+ CMSY8 CMTI12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips PS2 -o PS2.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2006.02.03:0854...

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Coursehero >> New York >> Cornell >> P 443

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%%Creator: %!PS-Adobe-2.0 dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: PS2.dvi %%Pages: 2 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMSS17 CMSS12 CMR12 CMMI12 CMEX10 CMSY10 CMMI8 CMR8 %%+ CMSY8 CMTI12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips PS2 -o PS2.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2006.02.03:0854 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 0ABF1D42C5DDD0C384C7E22F8F8047BE1D4C1CC8E33368FB1AC82B4E96146730 DE3302B2E6B819CB6AE455B1AF3187FFE8071AA57EF8A6616B9CB7941D44EC7A 71A7BB3DF755178D7D2E4BB69859EFA4BBC30BD6BB1531133FD4D9438FF99F09 4ECC068A324D75B5F696B8688EEB2F17E5ED34CCD6D047A4E3806D000C199D7C 515DB70A8D4F6146FE068DC1E5DE8BC5703D288CAFFEFC421ABEC649FD87E34B 8152B8403C7DB49860ED86B02711EE6E5B72D7D9B408B1FB89D5C1C78ACAA4A0 4E176AB7D7281992BE94DC902056793D2F8F189600650843FCB5CB77BDE88C4B 449C6606FAA7FCFF76CAC7E4A8EA5B049F569B412D5D48969EA632413B51E98D 85A05FB8FE1E1743AD1D04C94B0604C1CAF907B11D90CED1FF488E81A46ABF0D E8EA592B2BD018B422239E246BD0FE2191DC6463FFBD6E77C5890C19A99048AE 5550DA109BCA45072ADB589433BB470E7ACC83EF7BF2A08C9557D7272A7D255A 8071DFCDA4C740317954408363B898632536523620FDCE3B854E4F45C84359DC C2ED04F83675EFFB75856C5ADD5E2878BA3238755F1372BF32E121E6675B7FDE 32EE401B32E20F091C825C5269472B4DC330160E43D4553E1937B275F3E8AC26 00A42A8B0F2BB336A0C0DFB31DDC8607DBAED908DABC33C5D92E8742DE4A9B41 CC635A8E1EC65D52887BF0A5035708AEC9880C27EA8013BA964BA2DEA66FA181 B8B4B22EDDB394D5941D9D53F0CF7D0047D993C7BDA2C87408AC97F93948B7CB B9FC78828CFE36B2BC0EE4C13BF3FECF1F83B9C83464ECB5B205145D1135DB2B 7B8760D42F403DF16267859D9D86F6604C61201A92F25D24CCBD98D216757088 8F3E1FCAB6F455D63DBAA9168C204502737446B56EDBB3E5E110F2B768BF5346 853DBF1E504CAD91AF4DBA632A32CDD9DA8001FD62E6726F3AB05B4A0DD7FB23 D3A9FC089EAA90DCBAD2A0EFE3B6FF3270BB7D2E3DD42E12270E6F44D423890A 4AFE1229168FFF773607316448D8DDA7848E8A954D00630A1CE351CC330BF0B1 CED892E0102E39A26E5F3F5CA72590CEC17C85AC737718151732C8A46F825A53 0D738B421DC81E1E351C0B03EAFAD5838A996AB2DF849153980CEE7B71B2368B 0B67DE9C544C52A90818753B7567A057D5E972CA3C30D7CCA1770697C5909940 324AEC69ACAA73FA7DA50C0169E50434CCD8A60B68B754C76C8850F2DD92F369 8328F101B5483B1DBD8A8852ADBE49A259AE34BB824F815DDA56D5C9B29D15B4 F0BF05B5D689B6F93B518FCBBEBC64F6ED9FC738107F9A3487C874469E73D181 71A3DF04469012C27EBC20F991AFF97A0552F1061EAB0605DE7A57891A0AADD4 44F3EDF3114FF34D1F0056EEAFD9AAF38A8879505A07202EA54FC9626F83622F 3C08D8C09B1F3B0B731CC5937D0207BD48BC9C962D363F9560C5BEE0F024DBCD 18C55F3FB1892A39E79FFCE60D507CF5603C27D5FF0AE867FEECD71365AADDEE 83FC5F18FB3411263CF48E29156060FC13A184575C6045ED4A733E609EF25456 7ECDB69728E69E5C42622354E662CB52182E9A203ABF710CF9665306B6388073 9BC3D0A2C07A8D920122B34062645808D71B49E8148306A867BDD6CAA2C9B1C2 4669CC13BA4B226A8D978C30C9B886E0BFC1DF7087E129E1F9DECBE2E0AC3984 7619C3B5B52CBE09 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 26 /braceleftbigg put dup 88 /summationdisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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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 - 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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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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Cornell - HMWK - 661
P661 Homework # 9 Due Tuesday 11/16/04 Finish reading Chapter 10. Read Chapter 11. Part 111/04/04(1) Count the number of massless modes in both heterotic string models. Part 2: (2) We spent little time on the heterotic model. We shall not come ba
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 - LNS - 214
Physics 214 Assignment #3 Due Thursday, September 19 before 5:00 pm Reading for coming lectures: Young & Freedman, Sections 20.1-20-4; 19.6-19.9; 20.5. Skills to be mastered be able to convert between wavelength () and wavenumber (k = 2/); given th
Cornell - LNS - 214
Physics 214 Fall 2002 Problem Set #5, due 10/3Skills to be mastered be able to identify traveling wave solutions f (x - ct) and g(x + ct) and pick out the velocity; be able to use the general solution f (x - ct) + g(x + ct) to the wave equation to
Cornell - LNS - 214
Physics 214, Fall 2002 Assignment #iThis is not a real assignment; it does not need to be turned in. The questions are taken from last fall's Prelim 1. They may be useful as you prepare for our Prelim 1. 1. A damped oscillator is modeled as a mass m
Cornell - LNS - 214