Question about uncertainty princple?

[cragar]

Lets say I measure the z-component of a particles angular momentum, then I can't know for certain the x and y componets. So if I measure the Z componet to be 0, the x and y componets could be zero or not.
So is it impossible to say that the particles total angular mometum is zero meaning all the componets are zero. Would this violate the uncertainty principle?

 

[Drakkith]

Lets say I measure the z-component of a particles angular momentum, then I can't know for certain the x and y componets. So if I measure the Z componet to be 0, the x and y componets could be zero or not.
So is it impossible to say that the particles total angular mometum is zero meaning all the componets are zero. Would this violate the uncertainty principle?

No, as you do not know what the values are. That is what the principle means. They COULD be zero, or they might not be.

 

[cragar]

so i could measure one of the components at it could be zero but I won't know what the other components are .

 

[mquirce]

I have a question that has to do with HUP ---- at least i suppose.
Let say we have two unity electric charge far way from each other in a distance D= 3.481*10^7 They are in static position. THe potential energy of them is E = e^2 / D *eps.0 = h/1 erg.
Let suppose that will have another distance D1 = D+1 cm. I am in dilema to know how will be the potential energy: < h/1 or 0?

 

[Mike Pemulis]

So is it impossible to say that the particles total angular mometum is zero meaning all the componets are zero. Would this violate the uncertainty principle?

No, that's not true; measuring precisely 0 total angular momentum does not violate the uncertainty principle. For example, the S-orbitals in a hydrogen atom have exactly 0 angular momentum. This is allowed because the commutators for angular momentum have the "strange" form,

$$[L_x, L_y] = i\hbar L_z$$
$$[L_y, L_z] = i \hbar L_x$$
$$[L_z, L_x] = i \hbar L_y$$

And as you know, the uncertainty principle between two operators depends on the commutator:

$$\Delta A \Delta B = \frac{1}{2} |[A, B]|$$

So if all components are zero, they all can be measured simultaneously.

For nonzero L, by contrast, L² and L_z can be measured simultaneously, and from there you can deduce how much of the rest is distributed among L_x and L_y, but it is impossible to go further and resolve the two individual components.

 

[cragar]

ok thanks for you answer mike . And how do we measure the angular momentum of the S orbital in the hydrogen atom? Would we just do the Stern–Gerlach experiment?

 

[Drakkith]

I have a question that has to do with HUP ---- at least i suppose.
Let say we have two unity electric charge far way from each other in a distance D= 3.481*10^7 They are in static position. THe potential energy of them is E = e^2 / D *eps.0 = h/1 erg.
Let suppose that will have another distance D1 = D+1 cm. I am in dilema to know how will be the potential energy: < h/1 or 0?

Did you do the math with the new distance? What is the new value?