IV. HYDROGEN APPROXIMATION
The scientists on the faraway planet Xxzxy don’t know how to solve differential equations, but they do know how to differentiate and integrate, and they are also experts in the variational principle. They study the ground state of the Hydrogen atom (electron mass μ, potential V (r) = −e2/r, neglect spin) by using a Gaussian trial wavefunction of the
form (r) = Ne−k2r2 , where N is a normalization constant. What are their best estimates for k and for the ground state energy? How does their answer for the ground state energy compare to the correct value?
