Getting Started with Gaussian Wavepackets & Uncertainty Principle

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Discussion Overview

The discussion revolves around Gaussian wavepackets and their relationship with the Uncertainty Principle, focusing on foundational concepts, definitions, and equations relevant to these topics. Participants seek clarification on specific definitions and the general form of Gaussian wavepackets.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses confusion about the definition of delta-x in relation to RMS(x) and seeks foundational understanding.
  • Another participant asserts that delta-x = RMS(x) is simply a definition without deeper physical meaning.
  • There is a request for the general equation of a Gaussian wavepacket, with one participant suggesting it involves the free particle wave function multiplied by a Gaussian function.
  • Multiple participants suggest searching online for information about Gaussian wavepackets, with one noting difficulty in finding a general equation despite the suggestion.
  • A participant shares a link to a resource that discusses Gaussian wavepackets and mentions the existence of a time-dependent wave function in a textbook, but notes that the resource does not provide that specific equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the general equation for Gaussian wavepackets, and there is a mix of responses regarding the clarity of definitions and the availability of resources.

Contextual Notes

Some participants express uncertainty about the definitions and equations related to Gaussian wavepackets, indicating a need for further clarification and exploration of the topic.

Who May Find This Useful

Individuals interested in quantum mechanics, particularly those studying wave functions and the Uncertainty Principle, may find this discussion relevant.

thegaussian
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I'm starting a project on Gaussian Wavepackets, and the evolution of the Uncertainty principle with time, however after the summer I'm a bit rusty :s, so I have a few questions, if anyone could help that would be great.

Ok, first of all I see (and largely understand) that delta-x delta-p > h-bar/2, but I would like to know how delta-x = RMS(x)? It's probably basic but I need good foundations...

Also, what is the general equation for a gaussian wavepacket?

Any help would be great, thanks!
 
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delta-x = RMS(x) is the definition of delta-x. What else is there to understand? there's no physical meaning to the relation, its just what delta-x is defined as.

as for the general equation of the gaussian wavepacket, I believe it is just the free particle wave function multiplied by a gaussian function.
 
jtbell said:
Try a Google search for Gaussian wave packet. :smile:

Yea I was going to say that, except I actually tried doing that search and I just could not find a general equation for the gaussian wave packet.
 
The http://musr.physics.ubc.ca/~jess/p200/gwp/gwp.html that I see has a rather detailed discussion of Gaussian wave packets, including the derivation of an explicit form of the initial wave function for one.

A full, explicit, time-dependent wave function that contains the spreading is another matter. I know it's in at least one textbook, Morrison's "Understanding Quantum Physics." The link above doesn't have that, but it does have an equation for the width of the packet as a function of time.
 
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