Assignment:
Two identical spin-1/2 particles with mass m are in a one-dimensional infinite square-well potential with width a, so V(x)=0 for 0 <= x <= a, and there are infinite potential barriers at x=0 and x=a. The particles do not interact with each other; they see only the infinite square-well potential.
a) Calculate the energies of the three lowest-energy singlet states.
b) Calculate the energies of the three lowest-energy triplet states.
c) Suppose that the particles are in a state with wave function
psi(x_1, x_2) = (1/sqrt(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 particles in a triplet spin state or a singlet spin state? Explain.