Visualization of uncertainty principle [graphs]

[moniqu3]

Homework Statement

I'm looking for graphs or other sources of uncertainty principle visualization (I'm suppose to use a Fourier transform to solve it and present visualization in MS Excel... but one thing at a time).

Homework Equations

The Attempt at a Solution

Digged google in 3 languages. I get a lot of equations and theory but not even one graph or other visualization.

Sorry about grammar mistakes since it's not my first language.
P.S: Should I post it in Quantum Mechanics sub-forum ?
Thanks in advance for Your help .

 

[Nessdude14]

Edited slightly from wikipedia:

Above is Heisenberg's gamma-ray microscope for locating an electron (shown in blue). The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma-ray is shown in red. Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the wavelength λ of the incoming light.

Hope this helps.

 

[moniqu3]

Not exactly what I'm looking for but it will help too. Thanks
I still can't find any graph with Fourier transformation used to make visualization
@edit
Yay, I've found one :
http://www.ams.org/samplings/feature-column/fcarc-uncertainty
Very simple example but will work just fine.
Im looking for something more like this, bell curves.

Maybe someone have higher 'google skill' than me

 

[algebrat]

This is sort of what you are looking for.

What do you want to apply the Fourier transform to, the bell shaped curve? A wave packet? Several delta functions?

Will you be using software? I didn't know Excel was used for this type of thing, which parts can it handle, integrating?

 

[asteriatic]

Thank you for your question. Visualization of the uncertainty principle can be a challenging task, as it involves understanding both the mathematical equations and their physical implications. However, there are some resources that can help with visualizing this concept.

One way to visualize the uncertainty principle is through the use of wave packets. A wave packet is a localized disturbance in a wave, and it can be used to represent a particle in quantum mechanics. The uncertainty principle states that the position and momentum of a particle cannot both be known with absolute certainty. This means that as the wave packet becomes more localized (representing a more precise measurement of position), the spread of possible momentum values increases, and vice versa.

You can use MS Excel to plot a wave packet, with position on the x-axis and amplitude on the y-axis. As you vary the width of the wave packet, you will see that the amplitude becomes more concentrated near the center (representing a more precise measurement of position), but the spread of possible momentum values increases.

Another way to visualize the uncertainty principle is through the use of Heisenberg's microscope. This thought experiment involves shining a light on a particle to measure its position, but the act of shining the light also affects the momentum of the particle. You can use MS Excel to create a graph showing the relationship between the position and momentum of the particle, and how they are affected by the measurement process.

In addition to these visualizations, you can also find some helpful graphs and animations online. For example, the University of Colorado Boulder has a website called "The Physics of the Universe" which has a section on the uncertainty principle with some visualizations and interactive simulations. You can also search for "uncertainty principle animations" on YouTube to find some helpful videos.

Overall, visualizing the uncertainty principle can be a challenging task, but with some creativity and the use of resources like MS Excel and online simulations, you can develop a better understanding of this important concept in quantum mechanics. I hope this helps and good luck with your project!