1) Griff. 7.1b only. Before you solve the problem with the variational method, first use unit analysis to get a rough guess for the complete ground state energy, and also for <V>. (Show your work)

2) Griff. 7.3

3) Use the variational principle to estimate the ground-state energy of the three-dimensional harmonic uscillator, .

Important - please choose as trial wave function a hydrogenic ground state, that is,
Psi(r, theta, phi) = N Exp[-alpha r] Y0,0(theta,phi).
(The N is a normalization constant, alpha will be your variational parameter, and Y0,0 is the usual ground state angular wave function (it's just 1/Sqrt[4 Pi])

4) Griff. 7.7

Extra Credit: (As usual, if you do this, hand it in to me separately)

Use the variational principle to show that any arbitary 1-dimensional attractive potential will always have a bound state.