- #1
rustygecko
- 1
- 0
Homework Statement
I'm interested in the solution of an equation given below. (It's not a homework/coursework question, but can be stated in a similar style, so I thought it best to post here.)
Homework Equations
[itex] A \nabla^2 f(x)-Bf(x)+C \exp(-2x^2/D^2)=0 [/itex]
where A,B,C,D are constants.
I know the solution (or the solution that's relevant for me) is:
[itex]f(x)=\frac{D^2C}{4} \int_0^{\infty} \frac{kJ_0(kx)\exp(-D^2k^2/8)}{Ak^2+B}dk [/itex]
where [itex]J_0[/itex] is a zeroth-order Bessel function, but I'm not entirely sure how to get there.
The Attempt at a Solution
It seems like a starting point might be solving:
[itex] A \nabla^2 f(x)-Bf(x)=0 [/itex]
which looks like a Helmholtz equation and then modifying that solution, but I haven't been able to solve that so far.