Prove Kramers’ relation:

which relates the expectation values of r to three different powers (s,s-1, and s-2), for an electron in the state Ψnℓm of hydrogen. Rewrite the radial equation (Equation 4.53) in the form

and use it to express ∫(ur^suⁿ) dr in terms of (r³), (r^s-1), and (r^s-2). Then use integration by parts to reduce the second derivative. Show that

Take it from there.

Transcribed Image Text:

5¹²)-(2x+1)--[(2x+18²-²²-²) = 0. (7.113)