Following the approach of section 3.5 on page 35, show that Ïa.1 Ïa.2 is an eigenfunction of

Following the approach of section 3.5 on page 35, show that ψa.1 ψa.2 is an eigenfunction of the Hamiltonian for two spins with no coupling between them:

Hence find the corresponding eigenvalue (the energy); make sure that each step in your argument is clear and justified.
Show that ψa,1 ψa,2 is also an eigenfunction of the coupling term J12 1z 2z; find the corresponding energy.
Without further detailed calculations explain why ψa,1ψa,2 is an eigenfunction of the Hamiltonian for two spins with coupling

state the corresponding eigenvalue (energy).

Transcribed Image Text:

H, two spins, no coupl-ud. I 11こ+1 '0,2/2- Htwo spins = Uo.lh: + uos!), + J 12h:12c;