uncertainty in heisenbergs uncertainty principle

niehls

This might be a stupid question, but i seem to find different versions of this the more i look. I have a big exam tomorrow, and i have a slight problem. The thing is that our textbook says that Heisenberg's uncertainty principle is
dx x dp (larger or equal to) h
dt x dE (larger or equal to) h

looking through my notes, i find
dx x dp (larger or equal to) h/2pie
dt x dE (larger or equal to) h/2pie

and a search on the internet yield more versions, among them:
dx x dp (larger or equal to) h/4pie
dt x dE (larger or equal to) h/4pie

hmm. could someone please try to explain this discrepancy to me. And please hurry, exam tomorrow

Thanks

marlon

There is not much to say about that. The formula's above are the correct version. Sometimes, the first version that you wrote is also used. It can be done because it differs from the correct one only up to some constant. The meaning however (the uncertainty) is still represented here. But in the end, just use the "official" version above

regards
marlon

Hans de Vries

[tex] \Delta p \Delta x \geq \frac{\hbar}{2} \ \ \ \ \Delta E \Delta t \geq \frac{\hbar}{2} \ \ \ \ \ \ \ \ \ \ \ \ with \ \ \hbar = \frac{h}{2 \pi}[/tex]

The smallest possible value is found in the case of the
the Gaussian Function only. For any other function it is more.

Regards, Hans

dextercioby

Yeah,Marlon,you forgot about that 2 in the denominator...

It happens...

Daniel.

dextercioby

First of all,it's not "d",but "Delta=[itex]\Delta [/itex]",okay??

There's no "uncertainty in the uncertainty principle"... QM principles show the relations given by Hans...That's that...

Daniel.

PS.Actually,they are valid in a far more general sense...

niehls

i know it's delta, just wasn't in the mood for learning tex :)

ok, i still don't know which version to use in different scenarios. I expect questions similar to:

"In the strong interaction a particle is exchanged between the protons and neutrons in the nucleus. Knowing that the distance in which the strong force acts is 1.4e-15m, estimate the energy of the particle (with speed near light speed)?"

This is a simple example, but i still need to use the "correct" version of the uncertainty principle. which one would i use in this case?

oh, and uncertainty in the uncertainty principle was a joke from the beginning for those of you who didn't get that... cheesy.

jtbell

The value of the constant in the HUP depends on how you define "uncertainty". The standard way is to use the standard deviations of the probabilty distributions of the variables. In terms of expectation values:

[tex] \Delta x = \sqrt {<x^2> - {<x>}^2 } [/tex]

and similarly for p, which gives

[tex] \hbar / 2 = h / 4 \pi [/tex]

for the constant.

Sterj

http://www.people.vcu.edu/~rgowdy/mod/122/xmp4.htm#4
Why doesn't this guy need to put 10^-14 in this formula:
dx=(<x^2>-<x>^2)^(1/2) ?

dextercioby

What's the point??It wouldn't serve him anything...It would still leave him with one eq.and 2 unknowns.However,the HUP would do the trick and solve his problem...

Daniel.