(a) Use the recursion formula (Equation 4.76) to confirm that when l = n ‒ 1 the radial wa...

(a) Use the recursion formula (Equation 4.76) to confirm that when l = n ‒ 1 the radial wave function takes the form

(b)

and determine the normalization constant Nn by direct integration.

(b) Calculate r and r2 for states of the form ψn(n-1)m.

(c) Show that the “uncertainty” in r (σr) is r/y/√2n + 1 for such states. Note that the fractional spread in r decreases, with increasing n (in this sense the system “begins to look classical,” with identifiable circular “orbits,” for large n). Sketch the radial wave functions for several values of n, to illustrate this point.