I've had lectures on the thoery of this topic, but I've not been given any examples and I'm struggling with how to apply the theory to this homework question:
A particle is described by the normalised wave function
Si(x,y,z)=Ae^-h(x^2+y^2+z^2) where A and h are real positive constants.
Determine the probability of finding the particle at a distance between r and r+dr from the origin.
p=integral (mod[Si(x,y,z)])^2 dxdydz
The Attempt at a Solution
I thought that the wave function was supposed to involve complex numbers, but there's no i in the wave function? I thought i needed the conjugate of the wave function to find mod[Si(x,y,z)]?
I think once i find (mod[Si(x,y,z)])^2 i then need to integrate it over the volume of a spherical shell with radius r and thickness dr, so r^2=x^2+y^2+z^2 but I'm confused about how to compute this integral. Do i need to parametrise the variables?
I'm obviously not asking for someone to give me the solution, but I'm having a hard time figuring out where to start with this problem, so any help would be greatly appreciated.