Explain how the variational principle is used to assess the quality of a trial wavefunction. In a calculation on the B atom, the following trial wavefunctions were used:
(a): 1s 2s 2p 3s 3p 3d,
(b) 1s 2s 2p,
(c) 1s 2s 2p 3s and
(d) 1s 2s 2p 3s 3p.
Sketch the relative energies of these wavefunctions compared to the true energy and explain your reasoning for this ordering