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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