  The Born rule postulates that the probability of measurement in quantum
mechanics is related to the squared modulus of the wave function $\psi$. We
rearrange the equation for energy eigenfunctions to define the energy as the
real part of $\hat{E}\psi/\psi$. For an eigenstate, this definition gives a
constant energy eigenvalue. For a general wave function, the energy fluctuates
in space and time. We consider a particle in a one-dimensional square well
potential in a superposition of two states and average the energy over space
and time. We show that, for most cases, such an energy expectation value
differs by only a few percent from that calculated using the Born rule. This
difference is consistent with experimental tests of the expectation value and
suggests that the Born rule may be an approximation of spacetime averaging.
