Problem 10 note.

For problem 10 (HW3) you will need to use del^2 in spherical coordinates to calculate the K.E.. Since Psi100 does not depend on theta or phi, I think you can use the r part which I believe is:
$$(1/r^2) \frac {d} {dr} (r^2 \frac {d \psi_{100}} {dr})$$

Assuming that is correct, then one would start with the integral of:
$$\psi_{100} (r) (1/r^2) \frac {d} {dr} (r^2 \frac {d \psi_{100} (r)} {dr})$$
over all space. Use the Jacobian... I think it will cancel the r^2 outside the derivatives. Does that make sense?