# Separating Hamiltonian functions. Helium atom.

1. Jun 26, 2008

### scorpion990

I'm using McQuarrie's "Quantum Chemistry" book for a little bit of light reading. He included a proof of a theorem that states that if a Hamiltonian function is separable, then the eigenfunctions of Schrodinger's equation are the products of the eigenfunctions of the simpler "separated" equations... Anyway...

I just started studying the helium atom. Schrodinger's equation is written with two different laplacian operators, one that acts "only on the first electron", and one that acts "only on the second electron". However, the laplacian for both electrons is just a differential operator which contains a mixture of partial derivatives with respect to all three coordinates. I don't understand why you can assume that the first laplacian only acts "on the first electron". After all, a differential operator (D) acting on two functions (F and G):
D(F*G) is not F*D(G) if D contains derivatives which pertain to F.

Help?

2. Jun 26, 2008