Yi & S$` HR O q6 S HR - Department of Chemistry … & S$` HR O q6 S HR V G- `! q ! ! HR$ qJ 3Z n o q...
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Yi&S$`HROq6SHR VG-`!q!!HR$qJ3Z noqp9mYiT0S A;pdkha=5pYiT0H7A;=5 q=5!FCP$*H+1?q% _p2]MCPpD]/KCPgq nQ[o4@Nfp4@L&Ep #l@O@^8pMCP+1U!qMCP p4Sdk r '.bpθ φ p)\$`qW(CPMC Pj,: C-1 eq x = r sinθ cos φ y = r sinθsinφ (C.1) z = r cosθ BIXc"q r >< 0 ∞ pθ 0 πp φ 0 2π q : C-1 W(CPMCPq
Transcript of Yi & S$` HR O q6 S HR - Department of Chemistry … & S$` HR O q6 S HR V G- `! q ! ! HR$ qJ 3Z n o q...
![Page 1: Yi & S$` HR O q6 S HR - Department of Chemistry … & S$` HR O q6 S HR V G- `! q ! ! HR$ qJ 3Z n o q p9m Yi T0 S A; p dk ha =5 pYi T0 H7 A; =5 q =5 ! F CP$* H +1 ? q% _ p2] MCPpD]](https://reader042.fdocument.org/reader042/viewer/2022011800/5acfae7d7f8b9ad24f8cba6d/html5/page/1.jpg)
r θ φ
C-1
x = rsinθ cosφ
y = rsinθsinφ (C.1)
z = rcosθ
r 0 ∞ θ 0
π φ 0 2π
C-1
![Page 2: Yi & S$` HR O q6 S HR - Department of Chemistry … & S$` HR O q6 S HR V G- `! q ! ! HR$ qJ 3Z n o q p9m Yi T0 S A; p dk ha =5 pYi T0 H7 A; =5 q =5 ! F CP$* H +1 ? q% _ p2] MCPpD]](https://reader042.fdocument.org/reader042/viewer/2022011800/5acfae7d7f8b9ad24f8cba6d/html5/page/2.jpg)
dV = dxdydz = r2sinθdrdθdφ (C.2)
f(r)
f (r)V
∫ dV = dr dθ0
π
∫ dφ0
2π
∫ f (r)0
∞
∫ r2sinθ
= 4π0
∞
∫ r2 f (r)dr (C.3)
∇2 =∂2
∂x 2+∂2
∂y 2+∂2
∂z2
=1
r2∂∂r
r2∂∂r
⎛
⎝ ⎜
⎞
⎠ ⎟ +
1
r2sinθ∂∂θ
sinθ∂∂θ
⎛
⎝ ⎜
⎞
⎠ ⎟ +
1
r2sin2θ∂2
∂φ 2 (C.4)
r
© K. Saito, 06/05/2010
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