Heisenberg Indeterminacy (Uncertainty) Equation

[305670352]

Can someone explain what this point from week 3 lecture 1:

'stated qualitatively, there is a limit on the accuracy to which the momentum and position of a particle can be known simultaneously'

links to the Heisenberg Indeterminacy (Uncertainty) Equation?

I am a bit confused

[carterwink2K]

There is a simple relationship between the uncertainty in momentum and position of a particle.

This relationship is (delta p)(delta x) is greater than or equal to h/(4*pi).

What this means is that if we have a greater accuracy for the position of the particle, which means a smaller value for delta x, we are more uncertain about its momentum. For example, if we knew the exact position of the particle with 100% accuracy, it would be impossible to know the momentum as delta x would be equal to 0. You can plus in the uncertainties into this relationship to solve for the other unknown uncertainty.

[Janys Li - 1L]

Hi!
The definition you quoted is directly related to the expression of the Heisenberg Indeterminacy Equation: ΔX*ΔP>=h/4pi. The right hand side of the equation is a fixed number, so when either of the two variables on the left hand side increases, the other decreases. This means that when the degree of accuracy of one variable increases, the maximum degree of accuracy you can get with the other variable decreases.

[Tania Peymany 1A]

To add onto Janys, the reason the fixed side decreases when one or both of the variables increase is because if the range of what we are looking at increases, then there is more uncertainty on where the electron could be located or in which direction it has gone. Similarly, if the momentum increases, then the speed of the electron has increased, once again increasing the uncertainty of whether the electron is within that range. As the fixed side decreases, there is less certainty or more uncertainty.