### Expectation Values in Hydrogen States

An electron in the Coulomb field of a proton is in the state described by the wave function . Find the expected value of the Energy, , , and .

First check the normalization.

The terms are eigenstates of , , and , so we can easily compute expectation values of those operators.

Similarly, we can just square probability amplitudes to compute the expectation value of . The eigenvalues are .

The Eigenvalues of are .

Computing the expectation value of is harder because the states are not eigenstates of . We must write and compute.

Jim Branson 2013-04-22