極座標

極座標 $(R,\theta,\phi)$では $(h_1,h_2,h_3)=(1,R,R\sin\theta)$だから

$$\bigtriangleup = \frac 1{R^2\sin\theta} \{ \partial_R(R^2\sin\theta\partial_R) +\p... ...(\sin\theta\partial_\theta) +\partial_\phi(\frac 1{\sin\theta}\partial_\phi) \}$$ (2.16)

$$= \frac 1{R^2}\frac\partial{\partial R}R^2\frac\partial{\partial R}... ...tial{\partial\theta} +\frac 1{R^2\sin^2\theta}\frac{\partial^2}{\partial\phi^2}$$ (2.17)