Uncertainty principle: ∆px*∆x = h/2 = 1/2ħ = h???? Giving 5 stars?

Niko @Niko

May 2021 2 89 Report

Uncertainty principle: ∆px*∆x = h/2 = 1/2ħ = h???? Giving 5 stars?

How is this possible?

if ∆px*∆x = h/2

and ħ = h/2π

then how can h/2 = ħ

And ofc this is more obvious, how can ∆px*∆x = h/2 and then ∆px*∆x = h ??????????

I started to study quantum physics, and till now I had no problems, but this just looks so ridiculous. Can anyone explain in details how and why this is as it is?

Science & Mathematics / Physics

TSK

Verified answer

H.U.P. states that

In any simultaneous determination of the position and momentum of a particle, the product of the uncertainty ∆x in its position and the uncertainty ∆p in its (conjugate) momentum, namely ∆p ∆x is given by

∆p ∆x ≥ ħ/2

For x component (in 3D):

∆px ∆x ≥ ħ/2

THE PRODUCT ∆px ∆x WILL ALWAYS EXCEED ħ/2

NOW:

∆px ∆x ≥ h ≥ h/2 ≥ ħ/2

Note that it's NOT '='

It is '≥'

debydete

The descrepencies arise from how exactly the uncertainties in "p" and "x" are defined.

The accepted "rigorous" principle is one derived from a mean square deviation of the uncertainties,delta(p) and delta(x), giving (1/2)h bar.

Its not too serious of a problem because its an inequality, placing upper bounds on the product of the uncertainties and is primarily used for order of magnitude calculations.