Visualizing Spin Up/Down Probabilities of an Electron Wave Function

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SUMMARY

The discussion centers on visualizing the probabilities associated with the spin of an electron represented by the wave function psi = 3i|up> + 1|down>. The calculated probabilities indicate that the probability of spin up is 0.9 and spin down is 0.1. To effectively represent these probabilities, a bar graph is the appropriate visualization method, confirming that spin up should be depicted with a value of 0.9 and spin down with a value of 0.1. This approach is validated as the correct method for displaying the discrete variable of electron spin probabilities.

PREREQUISITES
  • Understanding of quantum mechanics concepts, particularly wave functions.
  • Familiarity with the representation of quantum states using Dirac notation.
  • Knowledge of probability distributions and their graphical representations.
  • Basic skills in data visualization, specifically using bar charts.
NEXT STEPS
  • Study the mathematical formulation of wave functions in quantum mechanics.
  • Learn about Dirac notation and its applications in quantum state representation.
  • Explore probability theory, focusing on discrete probability distributions.
  • Investigate data visualization techniques using tools like Matplotlib or Excel for creating bar graphs.
USEFUL FOR

Students and professionals in physics, particularly those specializing in quantum mechanics, as well as data scientists and educators looking to visualize quantum probability distributions.

Hyperreality
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A wave function psi = 3i|up> + 1|down> corresponding to the spin of the electron.

If I want to draw the distribution of the measured outcome, do I do the following?Probability of spin up = 0.9

Probability of spin down = 0.1

So I would draw a bar graph showing that spin up has a value of 0.9 and spin down have a value of 0.1. Is this right?
 
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Hyperreality said:
A wave function psi = 3i|up> + 1|down> corresponding to the spin of the electron.

If I want to draw the distribution of the measured outcome, do I do the following?


Probability of spin up = 0.9

Probability of spin down = 0.1

So I would draw a bar graph showing that spin up has a value of 0.9 and spin down have a value of 0.1. Is this right?

Yes. Since it is a discrete variable, the only way to plot the probabaility distribution is as a bar chart.
 

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