- #1
zhuang382
- 10
- 2
- Homework Statement
- What is ∇^2ln s in two dimensions where s =√x2+y2
- Relevant Equations
- delta function homework problem
My intuition for this problem is to use divergence theorem:
## \int_V \nabla^2 u dV = \int_S \nabla u \cdot \vec{n} dS##
But note that ##\vec{n}## is perpendicular to x-y plane, and makes ##\int_S \nabla \ln s \cdot \vec{n} dS = 0##
If we take laplacian in polar coordinate directly, then ##\nabla^2 \ln s = 0##
Can someone helps me on this?
## \int_V \nabla^2 u dV = \int_S \nabla u \cdot \vec{n} dS##
But note that ##\vec{n}## is perpendicular to x-y plane, and makes ##\int_S \nabla \ln s \cdot \vec{n} dS = 0##
If we take laplacian in polar coordinate directly, then ##\nabla^2 \ln s = 0##
Can someone helps me on this?