Given the following space part of an approximate wave function for the Li^+ ion:

Question

Given the following space part of an approximate wave function for the Li^+ ion: 1/Squareroot 2 [1s(1)2p_1(2) + 2p_1(1)1s(2)] (e) Write a physically possible spin part for this wave function. (f) What energy would this state have if the 1/r_12 electron repulsion term in H did not exist? Express your answer in units of Ry (Rydberg). (g) Describe qualitative how and why the energy of the state changes if the 1/r_12 term in H is included. (h) Determine the eigenvalue of the total spin angular momentum operator squared S^2 for the Li^+ ion in the state described by equation (2), including the spin part determined in (e). (i) Define Hund's rule and justify it on the basis of the antisymmetry condition for fermion wave functions.

Explanation / Answer

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

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