Answer Happy

B2) A one-dimensional infinite potential well of length L is described by the potential 10 0SXSL V(x) = +0 elsewhere The normalized eigenfunctions of a particle in the potential V(x) are nex sin L OSXSL n=1,2,3.... elsewhere Consider the motion in the potential well of a system of three distinguishable particles with the same mass M and with coordinates x, x, and x; respectively a) Write the energy and the wavefunction of the ground state of this system; show that the ground state is not degenerate. [5 marks) 3L 1 - 11,186 * - 4)+1,186 : _*)+av,18(*» -«) 4 b) Use time-independent non-degenerate perturbation theory to calculate the energy shift of the ground state to first order due to the following perturbations: 1) Å, = 2 [7 marks] ii) #2 = 1V,L8(x - x)+11,L8(x2 - xy + 2V.L8(x3 - x) where i<1 and V, is a constant, [12 marks) c) Propose a perturbation that does not shift the energy level of the ground state of the three particle system to first-order. Justify your choice. [6 marks] PZ