513.001 Molecular and Solid State Physics

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Physical
Constants

Periodic System
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Variational approach

Consider as a variational approximation to the ground state of the hydrogen atom the wavefunction, $\psi(r) = \exp(-\alpha r)$. Calculate the corresponding energy $E(\alpha )$ by substituting the wavefunction into the Schrödinger equation for hydrogen. Then minimize the energy with respect to the parameter $\alpha$. Compare your result with the exact solution.