# variation method applied to hydrogen atom

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In the case of the hydrogen atom, with four hyperfine levels IF, MF) which are X1,1), X1,0), 1l,-1) and X0,0), fig. I computed numerically the ground state energy of hydrogen by variational procedure, firstly expanding the wave function over the s-wave basis set STO-3G $$\psi(r)=\sum_{i=0}^3 C_{i} e^{-\alpha_ir^2}$$ and then solving the generalized eigenvalue problem (in matrix notation) $$\textbf{HC}=E\textbf{SC}$$ As output I have all 3x3 matrices. Researchers have developed a highly effective, environmentally friendly method for converting ammonia into hydrogen. The new technique is â¦