δ2Test for Atomic Wave Functions, Applied onH

Abstract

In searching for an extremum principle for wave functions, which meets the needs of oscillator strength calculations better than the energy minimum principle, one thinks of ${\delta }^2=\int {\mathrm{}\left[\right(H-E\left)\mathrm{}\psi \right]}^{2}d\tau =min$. However, according to an estimate of James and Coolidge this should not give good results. An example, the ground state of H, is calculated with a simple approximation function, and demonstrates the truth of this assumption. It suggests that the best oscillator strengths are still achieved by ($E=min$) wave functions with the dipole velocity formula.