uncertainity principle

[jimmyjammy]

can you let me know the heisenberg's uncertainity principle in spherical coordinates or atleast share a link from which i can get it

Edited June 13, 2013 by jimmyjammy

[mathematic]

http://en.wikipedia.org/wiki/Uncertainty_principle

 

The quantities involved are scalars and don't depend on coordinate system.

[jimmyjammy]

i have a wave function in spherical coordinates and i'll have to see if it obeys the uncertainity principle. then how do i do it without converting the wave function into cartesian coordinates???

[ajb]

I take it you want to show

 

[math]\sigma_{A}\sigma_{B} \geq \frac{1}{2} \left| \langle [A,B]\rangle \right|[/math]

 

or something similar, where A B are Hermitian operators and we have your state defining the experctation value?

 

It looks like a computational problem invloving integration in sphereical coordinates.

 

I will just say that for the uncertainty principle, in general, you need a state (pure or mixed) and two Hermitian operators. States by themselves do not "obey the uncertainty" as such.

Edited June 14, 2013 by ajb