Statistical form of Heisenberg Uncertainty

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SUMMARY

The discussion centers on the statistical interpretation of the Heisenberg Uncertainty Principle, specifically regarding the assumption of a normal (Gaussian) distribution in the context of photon detection. The participants explore the implications of detecting a single photon within a resonant LC network, where the energy of the photon is defined as E = hf. The goal is to ascertain the momentum distribution of detected photons and whether superposing multiple distributions can yield a sinusoidal waveform, which is a classical expectation from such systems.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle
  • Familiarity with quantum mechanics and photon behavior
  • Knowledge of resonant LC circuits
  • Basic statistics, particularly Gaussian distributions
NEXT STEPS
  • Research the implications of the Heisenberg Uncertainty Principle in quantum mechanics
  • Study the properties of Gaussian distributions in statistical mechanics
  • Explore the behavior of photons in resonant LC networks
  • Investigate methods for superposing wave functions in quantum systems
USEFUL FOR

Physicists, quantum mechanics students, electrical engineers, and anyone interested in the statistical properties of photon detection and wave behavior in resonant systems.

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I don't like to assume things without checking..

Is the distribution really a 'normal distribution' aka Gaussian? Is this an experimental result or a 'good enough' assumption?
 
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You must be talking about something specific... but left us guessing what.
Could you elaborate ?
 
Elaborate, yes of course, sorry.. I knew what I meant, at least I thought I did..

In the background is an LC network resonant at f primed with N photons of energy E ( = h f ) . We 'know' from the classical result that that radiation from any point in this network will 'look' sinusoidal. In fairness to the people who are kind enough to give time to this forum the question has to be simple.. the whole population is my problem..

Basically .. when I have detected a single photon at (say) x then I hoped to be able to say that the momentum (indirectly the energy) lies within the range given by a distribution of the form Xbold where Xbold is the answer to the question.

By superposing a lot of Xbolds .. hopefully I'd get my sinewave back. A vain hope? Xbold remains the answer to the intended question.. anything extra is a bonus.
 

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