Let say I have prepared two identical particle, both describable by a wavefunction Psi, whereby,(adsbygoogle = window.adsbygoogle || []).push({});

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?"

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# Hamiltonian in experiments

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