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

In summary, the uncertainty principle states that the product of the uncertainties in position (Δx) and momentum (Δp) must be greater than or equal to Planck's constant divided by 4π. This condition is satisfied in the Gaussian wave function and a more general class known as "coherent states." These states are minimal uncertainty wave packets that remain minimal under time evolution and have expectation values for position and momentum that satisfy classical equations of motion. This makes them useful for studying the classical limit of quantum mechanics.
  • #1
bs vasanth
16
1
When it actually 'equal to' in uncertainty principle?
For example under what conditions:
ΔxΔt = h/4[itex]pi[/itex]
 
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  • #2
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 dependant 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."
 
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  • #3
Your statement of the uncertainty principle should read ΔxΔp.
 

1. What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics which states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.

2. Who discovered the uncertainty principle?

The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927 as part of his work on quantum mechanics.

3. How does the uncertainty principle affect our understanding of the physical world?

The uncertainty principle challenges our classical understanding of the physical world by showing that there are inherent limitations to our ability to measure and predict the behavior of particles on a quantum level. It also highlights the role of probability and randomness in the behavior of particles.

4. Can the uncertainty principle be observed in everyday life?

No, the uncertainty principle is only applicable on a quantum level and cannot be observed in our everyday macroscopic world. It is only observed in the behavior of particles at the subatomic level.

5. How does the uncertainty principle relate to the concept of wave-particle duality?

The uncertainty principle is closely linked to the concept of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behaviors. The uncertainty principle shows that it is impossible to know both the position and momentum of a particle at the same time, highlighting the wave-like behavior of particles on a quantum level.

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