When does ΔxΔp equal h/4pi in the uncertainty principle?

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SUMMARY

The uncertainty principle states that ΔxΔp equals h/4π under specific conditions, particularly when utilizing Gaussian wave functions and coherent states. Coherent states represent minimal uncertainty wave packets that maintain their minimality during time evolution, aligning with classical equations of motion. This principle is crucial for understanding the classical limit of quantum mechanics, as detailed in the provided resources.

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When it actually 'equal to' in uncertainty principle?
For example under what conditions:
ΔxΔt = h/4[itex]pi[/itex]
 
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The Gaussian is an example of a wave function in which the equality is satisfied.

A more general class are called "coherent states".
http://www.indiana.edu/~ssiweb/C561/PDFfiles/Uncertainty2008.pdf
http://www.fysik.su.se/~hansson/KFT2/extra notes/cstates copy.pdf

From the first of the above two links:
"In summary, we have seen that the coherent states are minimal uncertainty wavepackets which remains minimal under time evolution. Furthermore, the time dependent expectation values of x and p saties the classical equations of motion. From this point of view, the coherent states are very natural for studying the classical limit of quantum mechanics."
 
Last edited:
Your statement of the uncertainty principle should read ΔxΔp.
 

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