Given the following space part of an approximate wave functi

Given the following space part of an approximate wave function for a Li^+ ion 1/squareroot 2 [1s(1) 2p_1(1) 1s(2)] Write a physical acceptable spin part for this wave function. If the 1/r_12 term in the hamiltonian is neglected, what would the energy be?

Solution

Since the space part is symmetric we need an antisymmetric spin part. Therefore, the spin-space wavefunction is = (1 / 2) [1s(1)2p1(2) + 2p1(1)1s(2)] (1 / 2) [ ]

If we ignore repulsion we have E approx = E1s + E2p = 9/2 9/8 = 45/8