Getting Started with Gaussian Wavepackets & Uncertainty Principle

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In summary, the conversation discusses the topic of Gaussian Wavepackets and the Uncertainty principle. The speaker has some questions about the definition of delta-x and the general equation for a gaussian wavepacket. They also mention a Google search for more information on Gaussian wave packets, but struggle to find a complete and explicit time-dependent wave function.
  • #1
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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  • #2
delta-x = RMS(x) is the definition of delta-x. What else is there to understand? Theres 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.
 
  • #3
Try a Google search for Gaussian wave packet. :smile:
 
  • #4
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.
 
  • #5
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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1. What is a Gaussian wavepacket?

A Gaussian wavepacket is a wavefunction that describes a particle's position and momentum in quantum mechanics. It is a mathematical function that has a Gaussian shape and represents the probability of finding a particle at a specific position and time.

2. How is a Gaussian wavepacket created?

A Gaussian wavepacket can be created by combining two or more plane wave functions with different frequencies and amplitudes. This combination results in a wavefunction that is localized in space and has a Gaussian shape.

3. What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle simultaneously. In other words, the more precisely we know one quantity, the less precisely we can know the other.

4. How does the uncertainty principle relate to Gaussian wavepackets?

The uncertainty principle is closely related to Gaussian wavepackets because the width of a Gaussian wavepacket is directly proportional to the uncertainty in position and momentum of a particle. A narrower wavepacket means a more precise position, but a wider wavepacket means a less precise position.

5. What are some applications of Gaussian wavepackets and the uncertainty principle?

Gaussian wavepackets and the uncertainty principle have many applications in various fields, such as quantum mechanics, optics, and signal processing. They are used to study the behavior of particles in quantum systems and to design efficient communication systems. They are also used in medical imaging to improve the resolution and accuracy of images.

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