Unformatted text preview: ~ N satisﬁes the following commutation relations with the angular momentum generators d ~ N dt = h H, ~ N i = 0 , ± L i ,N j ² = i ~ e ijk N k , ± N i ,N j ² = i ~ e ijk (2 mH ) L k where ~ N = 1 2 ³ ~ p × ~ L~ L × ~ p ´me 2 r ~ r. 3 . Two spin 1 / 2 particles interact via the Hamiltonian H = J ( S x 1 S x 2 + S y 1 S y 2 + kS z 1 S z 2 ) where J,k are constants. Find the energy levels of this system and their degeneracies. Discuss separately the cases where the spatial wavefunction is symmetric and antisymmetric under exchange of the two electrons. 4 . S15.3.3 5 . S15.3.4 6 . S15.3.5 1...
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 Spring '10
 Sghy
 mechanics, Angular Momentum, Energy, Momentum, 2m

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