- #1
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Let say I have prepared two identical particle, both describable by a wavefunction Psi, whereby,
Psi = a*1 + b*2, where, 1 and 2 are two stationary wavefunctions.
If I perform an experiment to find out the systems' energy, this is equivalent to operating a Hamiltonian on Psi. Operating,
HPsi = H(a*1 + b*2) = a*E1*1 + b*E2*2
where, E1 is eigenvalue with eigenfunction 1,
E2 = eigenvalue with eigenfunction 2.
That means, I might get energy = E1 for the first particle from the experiment, and
energy = E2 for the second particle.
How can we get two different energy value E1 and E2 when I prepared both the particles exactly the same and both have the same wavefunction. So they must give me the same energy.
Otherwise, where does the energy difference E1-E2 come from?"
Psi = a*1 + b*2, where, 1 and 2 are two stationary wavefunctions.
If I perform an experiment to find out the systems' energy, this is equivalent to operating a Hamiltonian on Psi. Operating,
HPsi = H(a*1 + b*2) = a*E1*1 + b*E2*2
where, E1 is eigenvalue with eigenfunction 1,
E2 = eigenvalue with eigenfunction 2.
That means, I might get energy = E1 for the first particle from the experiment, and
energy = E2 for the second particle.
How can we get two different energy value E1 and E2 when I prepared both the particles exactly the same and both have the same wavefunction. So they must give me the same energy.
Otherwise, where does the energy difference E1-E2 come from?"