As the Uncertainty Principle suggests that $\Delta x\Delta p\geq h/4\pi$, a particle must have different velocities at any point in space within it's Gaussian distribution. Since wave functions describes particles, the wave function should also have an uncertainty in velocity which should lead to dispersion. I would like to know why don't free particles disperse and the chasm in my understanding.
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Mozibur Ullah
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Wave function does not have a definite velocity (unless it is an eigenfunction if velocity) - this is the expression of the uncertainty in velocity, i.e. the dispersion. HUP isa simplified version of it. – Roger V. Sep 26 '21 at 04:50
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Possible duplicate: https://physics.stackexchange.com/q/54534/2451 – Qmechanic Sep 26 '21 at 04:55