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The Uncertainty Principle and Fourier Transforms
Specialized IPython/Jupyter Notebook material developed by Mara Casebeer and Alex Frano - Published November 29, 2023
DOI: 10.1119/PICUP.Exercise.UncertaintyPrinciple
In this exercise, students will use Discrete Fourier Transforms (DFTs) to visualize the Heisenberg Uncertainty Principle. They will gain practice with NumPy and Matplotlib by plotting Gaussian functions, constructing wave packets, and computing DFTs using NumPy's Fast Fourier Transform (FFT). Finally, students will analyze the relationship between the shape of a wave packet and its Fourier transform, connecting these concepts to the Heisenberg Uncertainty Principle.
| Subject Area | Quantum Mechanics |
|---|---|
| Level | First Year |
| Specialized Implementation | IPython/Jupyter Notebook |
| Learning Objectives |
* Import relevant packages and define variables (Exercise 1 and Exercise 2)
* Explore the parameters of a Gaussian function by plotting using matplotlib (Exercise 2)
* Construct a wave packet using a Gaussian function and a sinusoidal function (Exercise 3)
* Explore how to make wide and narrow wave packets and plot them (Exercise 3)
* Create wave packets and then take the fourier transform using numpy's fast fourier transform (Exercise 4)
* Compare the fourier transforms of wave packets of different widths and frequencies (Exercise 4)
* Explain how the width of the wave packet and the width of the Fourier transform are related and how this demonstrates the uncertainty principle (Exercise 5)
|
| Time to Complete | 60 min |
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Credits and Licensing
Mara Casebeer and Alex Frano, "The Uncertainty Principle and Fourier Transforms," Published in the PICUP Collection, November 2023, https://doi.org/10.1119/PICUP.Exercise.UncertaintyPrinciple.
DOI: 10.1119/PICUP.Exercise.UncertaintyPrinciple
The instructor materials are ©2023 Mara Casebeer and Alex Frano.
The exercises are released under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license
