Suppose that particles are in state with wave function psix

Suppose that particles are in state with wave function psi(x) = 1/squareroot 2 2/a[sin pi x_1/a sin 7 pi x_2/a + sin pi x_2/a sin 7 pi x_1/a] where x_1 is the position of particle 1 and x_2 is the position of particle 2. Are the particle in singlet spin state or triplet spin state? Explain.

Solution

Triplet states are symmetric under interchange of the labels 1 and 2, whereas the singlet state is antisymmetric.

Since we get back the same wavefunction when we interchange 1 and 2 this wavefunction represents a triplet state.