HW 13: Multi-Electron Systems
Question-1 ¶ Specify weathe the following wavefunctions are symmetric or anti-symmetric with respect to exchange of electrons. Also specify symmetry of spatial and spin parts
ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 ) ] ⋅ [ α ( 1 ) β ( 2 ) − β ( 1 ) α ( 2 ) ] \psi(1,2)=[1s(1)2s(2) + 2s(1)1s(2)]\cdot [\alpha(1)\beta(2) - \beta(1)\alpha(2)] ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 )] ⋅ [ α ( 1 ) β ( 2 ) − β ( 1 ) α ( 2 )]
ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 ) ] ⋅ [ α ( 1 ) α ( 2 ) ] \psi(1,2)=[1s(1)2s(2) + 2s(1)1s(2)]\cdot [\alpha(1)\alpha(2)] ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 )] ⋅ [ α ( 1 ) α ( 2 )]
ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 ) ] ⋅ [ α ( 1 ) β ( 2 ) + α ( 1 ) β ( 2 ) ] \psi(1,2)=[1s(1)2s(2) + 2s(1)1s(2)]\cdot [\alpha(1)\beta(2) + \alpha(1)\beta(2)] ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 )] ⋅ [ α ( 1 ) β ( 2 ) + α ( 1 ) β ( 2 )]
ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) − 2 s ( 1 ) 1 s ( 2 ) ] ⋅ [ α ( 1 ) β ( 2 ) + α ( 1 ) β ( 2 ) ] \psi(1,2)=[1s(1)2s(2) - 2s(1)1s(2)]\cdot [\alpha(1)\beta(2) + \alpha(1)\beta(2)] ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) − 2 s ( 1 ) 1 s ( 2 )] ⋅ [ α ( 1 ) β ( 2 ) + α ( 1 ) β ( 2 )]
ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 ) ] ⋅ [ α ( 1 ) β ( 2 ) + α ( 1 ) β ( 2 ) + α ( 1 ) α ( 2 ) ] \psi(1,2)=[1s(1)2s(2) + 2s(1)1s(2)]\cdot [\alpha(1)\beta(2) + \alpha(1)\beta(2)+\alpha(1)\alpha(2)] ψ ( 1 , 2 ) = [ 1 s ( 1 ) 2 s ( 2 ) + 2 s ( 1 ) 1 s ( 2 )] ⋅ [ α ( 1 ) β ( 2 ) + α ( 1 ) β ( 2 ) + α ( 1 ) α ( 2 )]
Question-2 ¶ What are singlet and triplet states?
How is Slater determinant enforce Pauli exclusion principle?
Write wavefunctions as Slater determinantscorresponding to ground and all the excited states of Li atoms specified by 1 s 2 2 s 1 1s^22s^1 1 s 2 2 s 1 1 s 1 2 s 2 1s^1 2s^2 1 s 1 2 s 2
Question-3 ¶ Question-4 ¶ Specify the possible J J J
1 P ^{1}P 1 P
4 F ^{4}F 4 F
2 G ^{2}G 2 G
1 H ^{1}H 1 H
Question-5 ¶ Write term symbols for the ground states of the following atoms. Show your work in finding S S S L L L J J J