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This manuscript is based on lectures given by Marshall Baker for a class on Mathematical Methods in Physics at the University of Washington in 1988. The subject of the lectures was Green’s function techniques in Physics. All the members of the class had completed the equivalent of the first three and a half years of the undergraduate physics program, although some had significantly more background. The class was a preparation for graduate study in physics. | Green s Functions in Physics Version 1 M. Baker S. Sutlief Revision December 19 2003 Contents 1 The Vibrating String 1 1.1 The String. 2 1.1.1 Forces on the String . 2 1.1.2 Equations of Motion for a Massless String . 3 1.1.3 Equations of Motion for a Massive String. 4 1.2 The Linear Operator Form. 5 1.3 Boundary Conditions. 5 1.3.1 Case 1 A Closed String. 6 1.3.2 Case 2 An Open String. 6 1.3.3 Limiting Cases . 7 1.3.4 Initial Conditions. 8 1.4 Special Cases. 8 1.4.1 No Tension at Boundary. 9 1.4.2 Semi-infinite String. 9 1.4.3 Oscillatory External Force . 9 1.5 Summary . 10 1.6 References . 11 2 Green s Identities 13 2.1 Green s 1st and 2nd Identities. 14 2.2 Using G.I. 2 to Satisfy R.B.C.15 2.2.1 The Closed String. 15 2.2.2 The Open String. 16 2.2.3 A Note on Hermitian Operators.17 2.3 Another Boundary Condition . 17 2.4 Physical Interpretations of the G.I.s. 18 2.4.1 The Physics of Green s 2nd Identity.18