Green Functio Green Functions in Finite 在有界空间 原则上仍然可以把空间内的电荷无限分割 由于边界条件的制约,在边界面上也会有 定的(单层或偶极层的)感生面电荷分布,也需 要将这些面电荷无限分割 为了唯一地确定(有界空间内)点电荷的电势, 也需要指定适当的边界条件 问题是:如何通过(适当边界条件下的),点电荷 电势的叠加,而给出任意电荷分布在任意边( 界条件下的电势
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition 3k.m KþE,±rmS>Öé du>.^§3>.¡þ¬k ½(ü½ó4)a)¡>Ö©Ù§I òù ¡>Öé /(½(k.mS):>Ö>³§ I½·>.^ ¯K´µXÛÏL(·>.^e):>Ö >³U\§ Ñ?¿>Ö©Ù3?¿> .^e>³ C. S. Wu 1Êù Green¼ê()
Green Functio Green Functions in Finite 在有界空间 原则上仍然可以把空间内的电荷无限分割 由于边界条件的制约,在边界面上也会有 定的(单层或偶极层的)感生面电荷分布,也需 要将这些面电荷无限分割 为了唯一地确定(有界空间内)点电荷的电势, 也需要指定适当的边界条件 ●问题是:如何通过(适当边界条件下的)点电荷 电势的叠加,而给出任意电荷分布在任意边(公 界条件下的电势
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition 3k.m KþE,±rmS>Öé du>.^§3>.¡þ¬k ½(ü½ó4)a)¡>Ö©Ù§I òù ¡>Öé /(½(k.mS):>Ö>³§ I½·>.^ ¯K´µXÛÏL(·>.^e):>Ö >³U\§ Ñ?¿>Ö©Ù3?¿> .^e>³ C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 数学问题:在有界空间 用定解问题 VG(r; r) ∈V 0 适当的边界条件 的解G(r;r)叠加出 的解(7),即用
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition êƯKµ3k.m ^½)¯K ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ), r, r 0 ∈ V ·>.^ )G(r; r 0 )U\Ñ ∇2u(r) = − 1 ε0 ρ(r), r ∈ V u Σ = f(Σ) )u(r)§=^ρ(r), f(Σ)9G(r; r 0 )L«Ñu(r) C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 数学问题:在有界空间 用定解问题 VG(r; r) ∈V 0 适当的边界条件 的解G(r;r)叠加出 v2u(r)=--p(r), ∈V 的解u(r),即用p(x)f(E)及G(x7)表示出(
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition êƯKµ3k.m ^½)¯K ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ), r, r 0 ∈ V ·>.^ )G(r; r 0 )U\Ñ ∇2u(r) = − 1 ε0 ρ(r), r ∈ V u Σ = f(Σ) )u(r)§=^ρ(r), f(Σ)9G(r; r 0 )L«Ñu(r) C. S. Wu 1Êù Green¼ê()
Green Functions in Finite 数学问题:在有界空间 用定解问题 VG(r; r) ∈V 0 适当的边界条件 的解G(r;r)叠加出 v2u(r)=--p(r), ∈V 的解α(r),即用川(r),f(∑)及G(r;T)表示出u(r)
Concept of Green Functions Green Functions in Time-Independent Problems Green Ftns of 3D Holmholtz eq. Superposition Principles in Infinite Space Green Functions in Finite Space: Definition êƯKµ3k.m ^½)¯K ∇2G(r; r 0 ) = − 1 ε0 δ(r − r 0 ), r, r 0 ∈ V ·>.^ )G(r; r 0 )U\Ñ ∇2u(r) = − 1 ε0 ρ(r), r ∈ V u Σ = f(Σ) )u(r)§=^ρ(r), f(Σ)9G(r; r 0 )L«Ñu(r) C. S. Wu 1Êù Green¼ê()