北大数学物理方法(A)-数学物理方程教案15Green函数1

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Outline1›ÊùGreen¼ê(˜)ÔnÆêÆÔn{‘§|2007cSC.S.Wu1›ÊùGreen¼ê(˜)OutlineùLJ:1Green¼êVgÃ.˜mU\nk.˜mSGreen¼ê½Â2­½¯KGreen¼ê­½¯KGreen¼ê˜„5ŸGreen¼êé¡5­½¯KGreen¼ê){3n‘Ã.˜mHelmholtz§Green¼ê){˜µ†¦)){µFourierC†C.S.Wu1›ÊùGreen¼ê(˜)OutlineùLJ:1Green¼êVgÃ.˜mU\nk.˜mSGreen¼ê½Â2­½¯KGreen¼ê­½¯KGreen¼ê˜„5ŸGreen¼êé¡5­½¯KGreen¼ê){3n‘Ã.˜mHelmholtz§Green¼ê){˜µ†¦)){µFourierC†C.S.Wu1›ÊùGreen¼ê(˜)OutlineùLJ:1Green¼êVgÃ.˜mU\nk.˜mSGreen¼ê½Â2­½¯KGreen¼ê­½¯KGreen¼ê˜„5ŸGreen¼êé¡5­½¯KGreen¼ê){3n‘Ã.˜mHelmholtz§Green¼ê){˜µ†¦)){µFourierC†C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.ReferencesÇÂÁ§5êÆÔn{6§§20.1—20.3ù&œ§5êÆÔn{6§§12.1nÎ!X1Á§5êÆÔn{6§§14.1,14.2,14.3C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:DefinitionùLJ:1Green¼êVgÃ.˜mU\nk.˜mSGreen¼ê½Â2­½¯KGreen¼ê­½¯KGreen¼ê˜„5ŸGreen¼êé¡5­½¯KGreen¼ê){3n‘Ã.˜mHelmholtz§Green¼ê){˜µ†¦)){µFourierC†C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definitionkޘ‡·|~fÃ.˜m¥k˜½Ö©Ù§Ö—Ýρ(r)3‹Ir0=(x0,y0,z0)Ndr0Sþ=ρ(r0)dr0§§3˜mr=(x,y,z):³´14πε0ρ(r0)|r−r0|dr0Šâ³U\n§r˜m¥ÜÖ)³U\å5§Ò3r:o³φ(r)=14πε0ZZZρ(r0)|r−r0|dr0C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definitionkޘ‡·|~fÃ.˜m¥k˜½Ö©Ù§Ö—Ýρ(r)3‹Ir0=(x0,y0,z0)Ndr0Sþ=ρ(r0)dr0§§3˜mr=(x,y,z):³´14πε0ρ(r0)|r−r0|dr0Šâ³U\n§r˜m¥ÜÖ)³U\å5§Ò3r:o³φ(r)=14πε0ZZZρ(r0)|r−r0|dr0C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definitionkޘ‡·|~fÃ.˜m¥k˜½Ö©Ù§Ö—Ýρ(r)3‹Ir0=(x0,y0,z0)Ndr0Sþ=ρ(r0)dr0§§3˜mr=(x,y,z):³´14πε0ρ(r0)|r−r0|dr0Šâ³U\n§r˜m¥ÜÖ)³U\å5§Ò3r:o³φ(r)=14πε0ZZZρ(r0)|r−r0|dr0C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definitionù‡(J`²µ‡ü :Ö3˜m³©Ù§@o§ÏLÖ©†U\§ÒŒ±?¿Ö©Ùž³ù«‰{ØL´|^ ‡©§‚55ŸC.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definitionù‡(J`²µ‡ü :Ö3˜m³©Ù§@o§ÏLÖ©†U\§ÒŒ±?¿Ö©Ùž³ù«‰{ØL´|^ ‡©§‚55ŸC.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definitionù‡(J`²µ‡ü :Ö3˜m³©Ù§@o§ÏLÖ©†U\§ÒŒ±?¿Ö©Ùž³ù«‰{ØL´|^ ‡©§‚55ŸC.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:DefinitionùLJ:1Green¼êVgÃ.˜mU\nk.˜mSGreen¼ê½Â2­½¯KGreen¼ê­½¯KGreen¼ê˜„5ŸGreen¼êé¡5­½¯KGreen¼ê){3n‘Ã.˜mHelmholtz§Green¼ê){˜µ†¦)){µFourierC†C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definition3k.˜mKþE,Œ±r˜mSÖÁ©du.^‡›§3.¡þ¬k˜½(ü½ó4)a)¡Ö©Ù§I‡òù¡ÖÁ©˜/(½(k.˜mS):Ö³§I‡½·.^‡¯K´µXÛÏL(·.^‡e):Ö³U\§‰Ñ?¿Ö©Ù3?¿.^‡e³C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definition3k.˜mKþE,Œ±r˜mSÖÁ©du.^‡›§3.¡þ¬k˜½(ü½ó4)a)¡Ö©Ù§I‡òù¡ÖÁ©˜/(½(k.˜mS):Ö³§I‡½·.^‡¯K´µXÛÏL(·.^‡e):Ö³U\§‰Ñ?¿Ö©Ù3?¿.^‡e³C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definition3k.˜mKþE,Œ±r˜mSÖÁ©du.^‡›§3.¡þ¬k˜½(ü½ó4)a)¡Ö©Ù§I‡òù¡ÖÁ©˜/(½(k.˜mS):Ö³§I‡½·.^‡¯K´µXÛÏL(·.^‡e):Ö³U\§‰Ñ?¿Ö©Ù3?¿.^‡e³C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:Definition3k.˜mKþE,Œ±r˜mSÖÁ©du.^‡›§3.¡þ¬k˜½(ü½ó4)a)¡Ö©Ù§I‡òù¡ÖÁ©˜/(½(k.˜mS):Ö³§I‡½·.^‡¯K´µXÛÏL(·.^‡e):Ö³U\§‰Ñ?¿Ö©Ù3?¿.^‡e³C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctionsinFiniteSpace:DefinitionêÆ¯Kµ3k.˜m^½)¯K∇2G(r;r0)=−1ε0δ(r−r0),r,r0∈V·.^‡)G(r;r0)U\Ñ∇2u(r)=−1ε0ρ(r),r∈Vu Σ=f(Σ))u(r)§=^ρ(r),f(Σ)9G(r;r0)L«Ñu(r)C.S.Wu1›ÊùGreen¼ê(˜)ConceptofGreenFunctionsGreenFunctionsinTime-IndependentProblemsGreenFtnsof3DHolmholtzeq.SuperpositionPrinciplesinInfiniteSpaceGreenFunctio

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