Once again, this ones a little harder.


1) wavefunction = (2- r/a_naught) e^(-r/a_naught)

2) wavefunction = r (sin theta) (cos phi) e^(-r/2a_naught)

For the first wavefunction, I multiplied out by the complex conjugate and got three separate integrals, I split them up and started with the least complex integral:

N^2 [4 int. e^[ (-2/a_naught) r ] dtao]

I used spherical coordinates to break it down, I ended up with:

4 pi N^2 int. (from 0 to inf.) of e^[(-2/a_naught) r] times r^2 dr

now i used integration by parts, yet somehow I ended up with getting infinite as one of my answers in the end. This function is an eigen function therefore it should spit out an eigenvalue in the end because the second part of the question asks you to show that the two equations in the beginning are mutually orthogonal(correct?).

I used these parts:

u = r^2
du= 2rdr
dv= e^[(-2/a_naught) r]dr
v = -a_naught/2 times e^[(-2/a_naught) r]

where did I go wrong?

help would be greatly appreciated, and if you could point me in the direction of the proper integral to use on an integral table that would help guide me as well.

Thanks in advance.