chem120a_ps7_sp07

chem120a_ps7_sp07 - Chem 120A Problem Set 7 Out: Tues....

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Chem 120A Problem Set 7 Out: Tues. April 17, 2007; Due: Fri. April 27, 2007 1. One very simple model for magnetic behavior is the Ising model. This assumes that electron spins in solids exist on separated sites and that the only interactions between spins are between nearest neighbors. In that case, the Hamiltonian is H Ising = J 1 2 i 6 = j s ( i ) z s ( j ) z , (1) where J is an exchange-type integral, s ( i ) z is the Z-component of the spin on site i , and the sum runs only over nearest neighbors. For the case of 2 sites on a line, find the four possible eigenstates of H Ising . Construct the energy level diagram of these eigenstates for the two cases of i) J < 0 (ferromagnet) and ii) J > 0 (antiferromagnet). Which of these cases has the greater total spin in the ground state? 2. This problem provides an exercise in using determinantal wavefunctions. As described in class, an N -electron electronic wavefunction can be written as a determinant of spin-space orbitals with nor- malization 1 ( N ! ) . Thus the wavefunction for the ground state of helium can be written as
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chem120a_ps7_sp07 - Chem 120A Problem Set 7 Out: Tues....

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