The discussion revolves around the increase of uncertainty in quantum mechanics, specifically focusing on the variance of the wave function over time and its relationship to Gaussian wave packets. Participants explore the mathematical representation of this phenomenon and the conditions affecting wave packet evolution.
Participants express differing views on the specifics of wave packet evolution, indicating that multiple competing models and interpretations remain in the discussion.
The discussion highlights limitations in understanding the exact conditions under which the variance increases, including dependencies on definitions and the specific forms of wave packets involved.
blue_leaf77 said:Are you talking about certain form of Gaussian wavepacket?
Hornbein said:it appears that the increase in the variance of the wave function over time is proportional to (1+t^2)1/2. Is that right?
The exact form involves some more constants as is pointed out by jtbell above.Hornbein said:I'm assuming it is a plain vanilla Gaussian, yes.
blue_leaf77 said:The exact form involves some more constants as is pointed out by jtbell above.
Not all wavepacket evolves in time that way, the temporal behavior depends on the form of the wavepacket itself and on whether the packet is in free space or not. If the packet propagates in a free-potential space, only the position basis wavepacket evolves - the momentum basis wavefunction remains unchanged. If, on the other hand, there is a varying potential, the wavepacket experiences a "force" and consequently the momentum basis wavefunction will also undergo a change in time in addition to the position wavepacket.