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I have a confusion right now. To the truth is, I have been studying QM for some years, but somehow, some of its concepts are still not really clear for me.

I understand that one of components of QM interpretation that generally accepted now is the Born postulate that [tex]\left|\Psi(x,t)\right|^2dx[/tex] is the probability to find the particle between x and dx.

Then the uncertainty principle [tex]\Delta x \Delta p_x \geq \frac{1}{2} \hbar[/tex] and [tex]\Delta t \Delta E \geq \frac{1}{2} \hbar[/tex], tells the inability to precisely measure two non-commuting observables simultaneously.

My confusion is here. For sure that we are able to calculate analytically the energy quantization of system such as H atom, with exact value.

So my question is like this.

If during the energy measurement of H atom, we get different spread results over time and also over position. Is this spread values are due to the uncertainty principle, or because the limitation of our tools in measurements (related to equipment accuracy, etc.), or because we are actually approaching the measurement that we treat the H atoms system as ensembles (so instead of pure QM, we actually doing measurement as explained by statistical mechanics)?? Where is the significance of the exact calculated H atom energy?

Sometimes, I still thinking that if we can calculate exactly the energy of the system, then, in every measurements, we should get the very same identical result.. is this way of thinking is wrong?

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# How to perceive probability value in QM?

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