# Does quantum randomness exist? [duplicate]

I just want to know if the quantum world is random. Or if the randomness is fully explained by measurement error. Or if it is just semantic.

The previous questions are open to interpretation and do not ask if "quantum randomness" is a scientific fact.

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The Schrödinger equation is a deterministic equation that describes how the probability distribution contained in the wave function changes over time. So for a normalized wave function $$\phi$$ the probability that the system described by $$\psi(t)$$ is in state $$\phi$$ at time $$t$$ is given by $$\bigl | \langle \phi \, | \, \psi(t) \rangle \bigr |^2$$. So if you pick \begin{align*} \phi(x) = \begin{cases} \frac{1}{\sqrt{\mathrm{Vol}(\Lambda)}} & x \in \Lambda \\ 0 & x \not\in \Lambda \\ \end{cases} \end{align*} for some volume $$\Lambda$$, then the above is the probability to find the quantum particle inside the volume $$\Lambda$$ at time $$t$$.