Quantum mechanics is non deterministic of actual measurements even in a gedanken experiment because of the Heisenberg Uncertainty Principle, which in the operator representation appears as non commuting operators. It is a fundamental postulate of quantum mechanics:
If you measure the position accurately, the momentum is completely undefined.
The interpretation of the solutions of Schrodinger's equation as predicting the behavior of matter depends on the postulates. Otherwise it would just be solutions of a differential equation. Quantum mechanics is postulates+mathematics.