hi all. i am trying to calculate the interaction between two excited hydrogen atoms, using degenerate perturbation theory. but comes up a few problems, any helps will be greatly appreciated. the perturbation has the form: H`=e3/R3(XaXb+YaYb-2ZaZb) where the R is the distancee between two atoms and a , b subscripts donates atom a and b respectively. i need to calculate the matrix elements have the form: (<ψaψb H` ψaψb> first thing is how to construct the total wave functions of the two atoms system? they add together or times together? and why? what is the physics meaning of: ψtotal=ψaψb ψtotal=ψa+ψb the second is, if using the exzact form, and ignor the radial funtion, is it possible to evaluate the matrix element? i.e for one atom in its 2 0 0 state and the other in its 2 1 0 state. then wavefunctions equal to theirs spherical harrmonics which are: 2 0 0 state = 1/(2* square root pi ) 2 1 0 state = square root 3 /(2* square root pi) * cosθ couples to one atom in 2 1 0 state and the other in 2 1 1 state 2 1 1 state = squre root (3)/2 * 1/(squre root (2* pi)) * sinθ*ei∅ the first term yields: ∫∫∫2 0 0 state * Xa * 2 1 0 state dr sinθ dθ d∅ *∫∫∫2 1 0 state * Xb * 2 1 1 state dr sinθ dθ d∅ since x= rsinθcos∅ and we have ignored the radial part, how can I evaluate dr ? above all, am I right for constructing the matrix element like the above way? Apologise for such a messy question, it is my first time to put equations up here, and I havent figured out how to construct a complex equation. Thank you in advance.