where is an normalized eigenfunction of the Hamiltonian
with eigenvalue , and an eigenfunction with eigenvalue
. If the energy of the particle is measured, what is the
chance of measuring the average of and ?
2
What else can you say for sure about the result of the
measurement?
3
What additional information would allow you to predict for sure
that the measurement will produce energy , if any?
4
If the energy of a large number of particles, each with the
above initial wave function, is measured, what can you say about the
results?
5
Suppose the wave function is initially
where is an normalized eigenfunction of the kinetic energy
operator with eigenvalue , and an eigenfunction with
eigenvalue . What are the chances of measuring the kinetic energy
to be ?