Consider three particles, each of mass m, moving in one dimension and bound to eachother by harmonic forces, i.e., V=k/2*[(x_1-x_2)^2+(x_2-x_3)^2+(x_3-x_1)^2]
1) Write the (time-independent) schrodinger equation for the system.
2) Transform to a new coordinate system (having the center of mass as one of the coordinates), so that one can readily solve for the energy eigenvalues and the corresponding eigenfunctions explicitly.
3) Using the result of 2), find the ground state energy if the particles are identical spin-0 bosons.
4) What is the ground state energy if the particles are identical spin-1/2 fermions?