Regarding the time-independent perturbation theory:
a) show that the 1rst order-corrected ground state energy e=e_0^(0)+e_0^(1) is an upper limit to the exact ground state energy e_0 of a perturbed system. (hint: use the variational theorem).
b) for the ground-state wavefunction, should the coefficients of the first-oder wavefunction correction generally increase or decrease in magnitude with increasing n? why or why not?
c) is the second order energy correction to the ground state e_0^(2) positive or negative?