Answer Happy

Three identical particles are in a one-dimensional harmonic oscillator potential well with classical angular frequency w. a. Write the complete time-independent Hamiltonian for this system, and express it in coordinate space as a differential equation whose solution is the three-body wave function V (x1,x2,x3). b. Assume the particles have zero spin. Use the single-particle wave functions to construct the ground-state wave function Vo(x1,x2, X3), and show that it satisfies the differential equation in (a), and find the ground-state energy. c. Assume the particles have spin . Repeat (b), and also construct the ground state spin state from single-particle spin eigenstates.