I noticed many PF threads mention ground state of Hydrogen atom. At the same time it is two body problem considered to be solved by separation of variables. It is true, of course, that we can find basis wave functions (solutions of Shroedinger equation). But why does anybody think, that ground solution is the member of this basis functions? Try find Google for theorem. You find nothing exact. Let us take "usual ground state" wavefunction of H atom with total momentum of atom P=0 Psi (R, r) level 1, L=0 (s orbital) Psi is the solution of Shroedinger equation where variables separated, where R is proton coordinate, and r is electron coordinate. Consider new function: Psi+=Psi(R, r) + Psi(R-x, r-x) where x is vector with |x| ~ 4* (atomic radius) Every physisist who deals with double quantum dot knows, that atom levels be repelled and Psi+ as trial variational function, gives lower energy, than initial Psi(R, r). Any comments?