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## Main Question or Discussion Point

Hi all, I have the following query:

I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to travel right over time.

However, is there any way to pinpoint the effects that a certain range of ##|\tilde{\Psi}|^2## has on ##|\Psi|^2##? For example, could one find out what effects momenta ##p ∈ [p_1,p_2]## have on the motion of ##|\Psi|^2##?

Thanks in advance!

I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to travel right over time.

However, is there any way to pinpoint the effects that a certain range of ##|\tilde{\Psi}|^2## has on ##|\Psi|^2##? For example, could one find out what effects momenta ##p ∈ [p_1,p_2]## have on the motion of ##|\Psi|^2##?

Thanks in advance!