Answer to Question #203518 in Quantum Mechanics for sphume

Question

Prove that the three triplet states are all symmetric and the singlet state is antisymmetric.

Answer 1

Triplet state is corresponding to S=1

So it Mas three possible configuration 1,0,-1.

Similarly single state corresponding to S=0

So it has only one possible spin configuration.

Since for fermionic system, wavefunction is always antisymetric. And space wave function is antisymmetric hence the spin wave function corresponding to triplet state must be symmetric.

Simlilarly for bosonic system wavefubction of the system is symmetric in nature and space wavefunction is antisymmetric so spin wavefunction corresponding to singlet state must be antisymetric.