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If after you apply an operator and hence calculate the expectation value of a measureable entity and if you get an eigenvalue, then does that mean when you do the measurement, you will always get the same value for that operator entity, each time?

I think yes because otherwise what is so special about eigenvalues. If no eigenvalues exist then it implies you will get any random number for that measurement but after an infinite number of measurements, you should get the average or expected value. However how do you calculate that average if after operating on psi does not give an eigenvalue?

I think yes because otherwise what is so special about eigenvalues. If no eigenvalues exist then it implies you will get any random number for that measurement but after an infinite number of measurements, you should get the average or expected value. However how do you calculate that average if after operating on psi does not give an eigenvalue?

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