# Hydrogen in equal superposition state

The problem: Suppose we know that a hydrogen atom is in equal superposition of 1s, 2s, and 2p states.
a) Write down the complete functional form for this state.
b) What is the expectation value of energy in this state?
c) What is the most probable value of L^2 operator?

I don't want the answer to the problem, but just a hint on where to start.

My ideas:
a) For part a, would I just right down the sums of the Spherical Harmonics with the Radial functions for the state, each with a 3 to the power of -1/2 in front?
b) For the expectation value of energy, would I just take the average of the three states?
c) For the L^2 operator, would I find out which quantum number l appears most then use that in the operator?

## Answers and Replies

Matterwave
Science Advisor
Gold Member
a) Sounds right to me
b) What do you mean average of the states? If you mean the average of the energies of the states, that sounds right to me too.
c)Find the most common l, and then find the eigenvalue that state corresponds with.

Thanks for the reply. I figured this problem was easier than it looked at first.