Hesienberg Uncertanity Principle

[Quarlep]

I watched a video about particle physics and there I saw something strange(for me) (link is here) and there in 13:44 I saw [x,y] I didnt understand because I think uncertanity principle exist only between position and momentum but he make uncertanity between two coordinates .Can somebody explain to me how [x,y] works.

Thanks

 

[tom.stoer]

He explicitly writes

[x,y] = 0
[p_x,p_y] = 0

So the uncertainty relation for x and y will read

\Delta x \; \Delta y = 0

Then he discusses the commutator for angular momentum.

[L_x,L_y] \neq 0

and from that one can derive an uncertainty relation for angular momentum.

 

[Quarlep]

so there's no problem

 

[tom.stoer]

no, there isn't

 

[Quarlep]

thanks

 

[PhysicistMike]

I watched a video about particle physics and there I saw something strange(for me) (link is here) and there in 13:44 I saw [x,y] I didnt understand because I think uncertanity principle exist only between position and momentum but he make uncertanity between two coordinates .Can somebody explain to me how [x,y] works.

Thanks

The expression [x, y] is called the commutator of x and y
http://en.wikipedia.org/wiki/Commutator

As you may know it's defined as [x, y] = xy - yx where x and y are any two operators. There's an uncertainty relation for any two observables A and B since [A,B] are what appear in the right hand side and the standard deviations of A and B appear on the left side of the inequality (uncertainty in Q = standard deviation in Q).

 

[MrRobotoToo]

An uncertainly relation holds between any two non-commuting observables.