# Hamiltonian in atomic units

 P: 43 1. The problem statement, all variables and given/known data So the question is I have to use some trial function of the form $$\sum c_if_i$$ to approximate the energy of hydrogen atom where $$f_i=e^{-ar}$$ for some number a (positive real number). Note that r is in atomic unit. 2. Relevant equations Because r is in atomic unit, I think I should use the Hamiltonian in atomic unit, that is $$H = -\frac{1}{2}\nabla^2 + \frac{1}{r}$$ or should I use the spherical Hamiltonian? I try to compute $$H_{ij} = \int_0^\infty f_iHf_j$$ but there will be the term $$\int_0^\infty f_1\frac{1}{r}f_2dr$$ which cannot be integrated (not converged). So what's wrong with the way I approach the problem? Thank you,
 P: 51 $$\int_0^\infty f_1\frac{1}{r}f_2dr$$ will converge if you change 1/r to 1/(r+eps)