Integrating exponential function in spherical polars
Hi. Just going over some past exam papers and can't work out how to answer one of the questions as the course notes only use simple examples.
I need to use variational method to estimate the ground state energy of a physical system using a trial wavefunction:
phi = Aexp(-Br/2a) [B and a constants]
I'm then asked to normalise phi using spherical polar coordinates to show
A^2 = (B^3)/(8.pi.a^3)
I know this is done by finding the integral of phi*phi d^3r between 0<r<a, 0<theta<pi and 0<phi<2pi but I'm not sure what to do with the exponental function in this integral.
Anyone have any ideas? Thanks for your help.