Average potential and kinetic energies for H ground state

[tententententen]

Homework Statement

Calculate the average potential and kinetic energies for the electron in the ground state of hydrogen.

Homework Equations

The Attempt at a Solution

I know that KE = E - <U(r)>. I know that E = (-KZ^2e^2)/(2a0) and I know that U(r) = -KZe^2/r but I can't figure out how to get the average potential energy from this so that the denominator is the same as the E and so that they can add together to get KE.

 

[MisterX]

You could always just calculate them directly by integration.
$$<KE> = \langle \psi \mid \frac{p^2}{2m}\mid \psi \rangle$$
$$<U> = \langle \psi \mid \frac{ke^2}{r}\mid \psi \rangle$$
You can also get some expectation values using the "Hellman-Feynman Theorem"
see https://en.wikipedia.org/wiki/Hellmann–Feynman_theorem#Expectation_values

 

[tententententen]

You could always just calculate them directly by integration.
$$<KE> = \langle \psi \mid \frac{p^2}{2m}\mid \psi \rangle$$
$$<U> = \langle \psi \mid \frac{ke^2}{r}\mid \psi \rangle$$
You can also get some expectation values using the "Hellman-Feynman Theorem"
see https://en.wikipedia.org/wiki/Hellmann–Feynman_theorem#Expectation_values

Thanks a lot! That makes a lot of sense. I appreciate it!