I have two question about variational method of quantum mechanics.
Why we always find the ground state energy by this approach. Why not the other excited states?
When we find the ground state energy of helium by this method, at one stage we consider $Z$ (charge of nucleus) is a variable parameter in stead of using "2". But we have done it because our analytical value was not matching with experimental value. My question is, if experimental value always guide us to modify the Hamiltonian, I mean if we use experimental value of ground state energy of helium at first place, then what is the benefit of this method? it sounds quite silly to me. If anybody can not understand me then I will edit my question. No problem. But give some response at least.