... 41 2. 2 Orbital angular momentum 41 2. 2.1 2. 2 .2 Eigenfunctions of orbital angular momentum 50 2. 2.3 Mathematical interlude: ... − 1) δn ,n 2 + (2n + 1)δn,n + (n + 1)(n + 2) δn ,n +2 (1.1 42) • ˆ n |p2 |n = m¯ ω − n(n − 1) h 2 δn ,n 2 + (2n + 1)δn,n − (n + 1)(n + 2) δn ,n +2 (1.143) Problem 18: • Show that if f (ˆ† ) is any ... differential equations d2 X + k2 X = dx2 d2 ψ + v2 k2 ψ = dt2 (1.170) whose boundary conditions become X(0) = X(L) = and corresponding solutions are respectively X(x) = c1 cos(kx) + c2 sin(kx) ψ(t) =...