What causes a particle to change directions

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A classical object changes direction due to a force, but the behavior of quantum particles is governed by uncertainty in their position and momentum until measured. Once measured, their state becomes uncertain again until the next measurement, with predictions relying on probabilistic laws. This inherent uncertainty is a fundamental property of quanta. The discussion also touches on whether a quantum's velocity fluctuates, suggesting it does not unless influenced by an external field, and notes that lost kinetic energy can convert to potential energy in such a field. The use of wave functions to describe particles is justified by their ability to yield accurate results, although the underlying reasons remain unknown.
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If a classical object changes direction it is done due to a force, but I'm much less certain about quanta. A quantum's position and momentum and uncertain until we measure it. After we measure it it becomes uncertain again until we measure it a second time. Between measurements its direction and momentum is uncertain and there is no law, except for probabilistic, statistical laws that can predict its next position between measurements. What causes this? Is it just a property of quanta that their position and momentum are uncertain? I'm pretty sure that's the answer but it's always good to double check.

One other thing, does a quantum's velocity fluctuate? If it slows down does it just convert that lost velocity and hence lost kinetic energy into potential energy?
 
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What causes this?
The evolution of the wave function.
Why do we use wave functions to describe particles? Because it gives the correct results.
Why? Nobody knows.

Is it just a property of quanta that their position and momentum are uncertain?
Right.

One other thing, does a quantum's velocity fluctuate?
I am not sure how you mean this, but the answer is probably "no" (unless you have an external field).

If it slows down does it just convert that lost velocity and hence lost kinetic energy into potential energy?
In an external field: Right.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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