How to find the information about position x and momentum p from this MATLAB figure?

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Aisha Mohamed
Aisha Mohamed 2023-8-18
回答： Raj 2023-9-4
I plotted the following Wigner function W(x,p) where (x) is the position and (p )is the momentum,
begin{equation}
f(x)=exp(-x^2+\lambda x+d)
\end{equation}
where $ \lambda \in \mathbb{C}$, $\mathbb{C}$ is the set of complex numbers,
My question is according this figure what information can we det about the position (x) and the momentum (p)/
I appreciate any help
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Aisha Mohamed
Aisha Mohamed 2023-8-18
This figuer is plotted to find Wigner distribution W(x,p) for the position (x) and the momentum (p) just I want to know what the color bar tell us about the position (x) and the momentum (p)?
Steven Lord
Steven Lord 2023-8-18
That picture tells me that your function is at its highest for values of x and p with small magnitude, and that the function drops off to visually negligible values pretty quickly (as you might expect for an exponential.)
If you're looking to somehow write a MATLAB function that "looks" at that plot and reverse engineers the equation that was used to create it, that's a much more difficult problem to solve than it is to describe.
If neither of those are the information you want to determine, you'll need to more clearly describe what exactly you're trying to figure out.

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Raj
Raj 2023-9-4
Hi ,
I am assuming you wanted to get an inference about the position and momentum from the graph of the particular entity.
According to ‘The Heisenberg uncertainty principle’, it is impossible to measure both the position and momentum of a particle with absolute precision.
As far as the Wigner distribution is considered, the graph uses a colour map to map the magnitude values to different colours. The colour map determines the specific colours used and the corresponding values they represent.
The "Parula" colormap is a perceptually uniform colormap introduced in MATLAB R2014b. It ranges from blue to yellow and is designed to provide better visibility and distinguishability.
Here is a rough description of the colour progression in the "parula" colormap:
  • Dark blue: Represents the lowest values.
  • Light blue: Gradually increasing values.
  • Green: Intermediate values.
  • Yellow: Higher values.
And as mentioned in the comments, we can see that the value of Wigner function is higher when the value of x and p are small.
You can refer to the documentation page to know more about colormap
https://www.mathworks.com/help/matlab/ref/colormap.html?searchHighlight=colormap%20array&s_tid=srchtitle_support_results_1_colormap%20arrayMathWorks%20India

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