I Doesn't the superposition in energy violate the conservation of energy

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Demystifier

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When the system is described as a superposition of two or more eigenstates of a hamiltonian (operator corresponding to the total energy of the studied system).

Can this eigenstates be interpreted as an energy of the studied system?
More precisely, it's the eigenvalue (not the eigenstate) that is interpreted as the energy. When physicists say "superposition of energies", they of course really mean superposition of Hamiltonian eigenstates with different eigenvalues.

Energy is an observable, not a state, isn't it?
Technically, Hamiltonian is an observable, energy is an eigenvalue of this observable.
 

vanhees71

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To be even more pedantic, and in this issue pedantry is quite necessary: The Hamiltonian is a self-adjoint operator representing the (total) energy of the system. The possible values the observable energy can take are the eigenvalues of that operator.

In the lab there are no Hilbert spaces and operators but some equipment measuring the energy of, e.g., a particle. The big detectors at the LHC have several different detectors allowing to measure the energy of particles. Nowhere is any abstract object like Hilbert spaces and operators to be seen! ;-))).
 
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In the lab there are no Hilbert spaces and operators but some equipment measuring the energy of, e.g., a particle
Yes of course, but equipment designed on the basis of our theoretical models to answer the questions we ask ourselves about what resists us and what we call "nature".

In all scientific rationality and rigors, we should also take into account the mediation of our brains, which is the starting point for any conscious scientific investigation for us human being. This is for all intellectual honesty.

/Patrick
 
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