# Uncertainties & Total Angular Momentum

• Sekonda
In summary, the conversation discusses determining an 'uncertainty' quantity using total angular momentum operators in the x,y, and z directions. The speaker is unsure of the correct approach but suggests using the commutation relations between the operators. They also clarify a mistake in their equation.
Sekonda
Hey,

My question is on determining an 'uncertainty' quantity using total angular momentum operators in the x,y and z directions where we know the commutation relations between the x,y and z directions of the total angular momentum operators.

I'm not really sure where to go with this at all, I let the commutator given act on a state |m> i.e. an eigenfunction of J(z)

$$[\hat{J_{x}},\hat{J_{y}}]|m>=i\hbar\hat{J_{z}}|n>=i\hbar m|m>$$

So the commutator must equal i*hbar*m, right? Anyway I'm not sure if this is even a correct way to begin, but it should be pretty straightforward however I haven't really come across a question like this before.

By the way I replaced subscripts 1,2,3 with x,y and z repsectively.

Thanks for any help!
SK

Sekonda said:
$$[\hat{J_{x}},\hat{J_{y}}]|m>=i\hbar\hat{J_{z}}|m>=i\hbar m|m>$$

not 'n' ket but 'm' ket.

Sorry...

SK

## 1. What is uncertainty in physics?

Uncertainty in physics refers to the lack of precise knowledge about the exact values of physical quantities. In other words, it is the degree of doubt or error associated with a measurement or calculation.

## 2. How is uncertainty represented in physics?

Uncertainty is typically represented using the symbol Δ (delta) followed by the name of the quantity. For example, the uncertainty in position would be written as Δx, while the uncertainty in velocity would be written as Δv.

## 3. What is total angular momentum in physics?

Total angular momentum is a physical quantity that describes the rotational motion of an object. It is the sum of the angular momenta of all the individual particles that make up the object.

## 4. How is total angular momentum calculated?

Total angular momentum is calculated by multiplying the moment of inertia of an object by its angular velocity. The moment of inertia is a measure of an object's resistance to changes in rotational motion, while angular velocity is the rate at which an object rotates.

## 5. How is uncertainty related to total angular momentum?

The uncertainty in total angular momentum is related to the uncertainties in the individual angular momenta and the uncertainty in the moment of inertia. As with any physical quantity, the uncertainty in total angular momentum will increase as the uncertainties in the individual components increase.

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