Provide a complete derivation of separation of variables for three identical
non-interacting particles 1, 2, and 3 of mass m with coordinates x1, x2, and x3
respectively in a box of length L. You may use the results from one-
dimensional particle in a box as presented in class and your text.
a. What is T(x1,x2,x3) in terms of T(x1), T(x2), and T(x3)?
b. What is V(x1,x2,x3) in terms of V(x1), V(x2), and V(x3)?
c. What is H(x1,x2,x3) in terms of H(x1), H(x2), and H(x3)?
d. What is \(\Psi(x1,x2,x3)\) in terms of \(\Psi(x1)\), \(\Psi(x2)\), and \(\Psi(x3)\)?
e. What is E in terms of E1, E2, and E3?
f. What is the normalization constant N in terms of N1, N2, and N3?