How to Simplify the Laplace Equation in Spherical Coordinates?

[physicss]

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.

 

[Grelbr42]

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 does the Laplace operator look like in spherical polar coordinates? If you then have this operator act on the following

f(r,θ,φ)=Rl(r)Ylm(θ,φ)

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)?

The buzzword is "separability." You can probably get quite a lot of help by googling this.

 

[kuruman]

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.

Can you state the problem that you still cannot solve?
According to our rules, to receive help, you need to show some credible effort towards answering the question. How about showing us what you tried and where you got stuck? We need something to work from.