SingletvstripletstatesPauli principlesaysthatthewavefunctionmustbe4(1,2)=-4(2,1);antisymmetric,Wavefunction iscomposed of spaceandspinparts;If the space part is symmetric, then the spin part must beantisymmetric;- Only one way to do this, singlet spin state· [α(1)β(2)-β(1)α(2)/21/2If the space part is antisymmetric, then the spin partmust be symmetric;- three ways to do this, triplet spin state: α(1)α(2)· [α(1)β(2)+β(1)α(2)/21/2·β(1)β(2)
Singlet vs triplet states • Pauli principle says that the wavefunction must be antisymmetric, (1,2)=-(2,1); • Wavefunction is composed of space and spin parts; • If the space part is symmetric, then the spin part must be antisymmetric; – Only one way to do this, singlet spin state • [a(1)b(2)-b(1)a(2)]/21/2 • If the space part is antisymmetric, then the spin part must be symmetric; – three ways to do this, triplet spin state • a(1)a(2) • [a(1)b(2)+b(1)a(2)]/21/2 • b(1)b(2) 7
SingletTriplet state[α(1)β(2)-β(1)α(2)/21/2[α(1)β(2)+β(1)α(2)]/21/2α(1)α(2)β(1)β(2)8
Singlet . Triplet state . [a(1)b(2)-b(1)a(2)]/21/2 a(1)a(2) [a(1)b(2)+b(1)a(2)]/21/2 b(1)b(2) - + 8