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I am sorry for the title, which seems to be into the philosophical discussions about reality going random in quantum scale. My aim is to approach the question in a definite and most reasonable, though basic way. Is quantum mechanics deterministic, if the equations allow to predict quantum state? The answer is: yes. Is this correct?
I cannot imagine how this cannot be correct and it is weird that there is so much internet discussion about this, doing so much harm to basic perception of physical reality. Wikipedia states what can help understand the doubts:
The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate.
However, the fact that some part of the system behaves in a particular way - a spread in this case - doesn't mean that it isn't deterministic. It just means that we do not have direct grasp on the particle in the equations, however it behaves predictibly, i.e. deterministically, because.. its evolution is predictable. Is this correct?