# Solitons and Heisenberg uncertainty

if we can find a 'soliton' solution for Nonlinear Schroedinguer equation , then does this imply that Uncertainty principle is false ??

since a soliton is a localized wave packet then i can find the position of the soliton and its momentum so apparently i have violated uncertainty.

Well, a soliton doesn't have to be localized that 'well'. It's only localized within a certain region - it would still 'carry some uncertainty'. The same goes for its momentum distribution. But then again, I'm not too familiar with the nonlinear schroedinger equation ;)

Matterwave
Gold Member
Solitons are localized, but they are still spread over some displacement, I don't get how you can violate the HUP.

A wave packet certainly does not violate the HUP, and non-dispersive wave packets certainly do not either.

Also, the Schrodinger equation is linear (otherwise superposition principle would not work), what's the nonlinear Schrodinger equation? what's the nonlinear Schrodinger equation? There are a family of equations called NSE, one of the most common is the http://en.wikipedia.org/wiki/Gross-Pitaevskii_equation" [Broken]. The unknown function in these equations is not a single particle wave function but rather a quantum field, so things like superposition, probability interpretation, uncertainty principle, etc must be abandoned or modified for this case.

To OP's question is just as false for solitons as it is for ordinary quantum wave packets, so my advice to the OP would be to further study single particle QM.

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If the position and velocity of the whole wave packet means
the position and velocity of one particle, this violates the uncertainty principle.

Because we can determine the position and momentum of the particle at the same time.

And the wave packet is spreading in all space as the particle is moving around and rebounds from the wall.

So the wave packet does not mean a particle.

There are a family of equations called NSE, one of the most common is the http://en.wikipedia.org/wiki/Gross-Pitaevskii_equation" [Broken]. The unknown function in these equations is not a single particle wave function but rather a quantum field, so things like superposition, probability interpretation, uncertainty principle, etc must be abandoned or modified for this case.

To OP's question is just as false for solitons as it is for ordinary quantum wave packets, so my advice to the OP would be to further study single particle QM.

That is, i have to present a paper about it in my Master , the question is what are these Nonlinear Schroedinguer equation used for ?? could someone give me an example

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if we can find a 'soliton' solution for Nonlinear Schroedinguer equation , then does this imply that Uncertainty principle is false ??

since a soliton is a localized wave packet then i can find the position of the soliton and its momentum so apparently i have violated uncertainty.

I just wanted to mention the Schroedinger's coherent states: they represent wave packets of a constant shape; thay are similar to solitons but are linear combinations of eigenstates (principle of superposition holds). Such states minimize the HU relationship. There applets on internet demonstrating that.

A certain average position R(t) does not mean there is no position spread in a wave packet.

Bob_for_short.

That is, i have to present a paper about it in my Master , the question is what are these Nonlinear Schroedinguer equation used for ?? could someone give me an example

The Gross-Pitaevski equation is used to describe weakly interacting bosons in an external potential. It can be used to describe bose condensates.