The discussion focuses on simplifying the Laplace equation in spherical coordinates using the function f(r,θ,φ)=Rl(r)Ylm(θ,φ). Participants emphasize the importance of understanding the Laplace operator's action on the function components, particularly how the radial part Rl(r) interacts with the angular part Ylm(θ,φ). The concept of "separability" is highlighted as a key principle for solving the problem, suggesting that breaking down the equation into its components can facilitate simplification.
PREREQUISITESStudents and researchers in mathematical physics, particularly those studying potential theory and partial differential equations, will benefit from this discussion.
What does the Laplace operator look like in spherical polar coordinates? If you then have this operator act on the followingphysicss said:Homework Statement: Hello, how can I simplify ∆f(r,θ,φ) by using f(r,θ,φ)=Rl(r)Ylm(θ,φ)?
Relevant Equations: f(r,θ,φ)=Rl(r)Ylm(θ,φ)
I know what the Laplace operator is and I also looked up how f(r,θ,φ)=Rl(r)Ylm(θ,φ) is defined but I still could not solve the problem.
what happens when the "r" part of the operator hits the "Y" part of the function? And similarly for the angle parts acting on Rl(r)?f(r,θ,φ)=Rl(r)Ylm(θ,φ)
Can you state the problem that you still cannot solve?physicss said:I know what the Laplace operator is and I also looked up how f(r,θ,φ)=Rl(r)Ylm(θ,φ) is defined but I still could not solve the problem.