Does Linear momentum operator and angular momentum operator

In summary, the conversation is discussing whether Px and Lx operators commute and whether taking a derivative with respect to a variable that is not present in the function results in a zero value. The cross product is also mentioned as a way to determine if the operators commute, and it is noted that [px, py] and [px, pz] both equal zero.
  • #1
hellomister
29
0

Homework Statement


Does Px Lx operators commute?

Homework Equations


This is just me wondering


The Attempt at a Solution


I tried doing this and I got something weird, my friend said that when you take a derviative with respect z or something that when you try to take the derivative of something that's not with respect to z it goes to 0. Is this true? p.s. I am not very good at math.
 
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  • #2
You tell me. L_x is made up of rs and ps. Which r and ps is L_x made of, and which r and ps does p_x commute with?
 
  • #3
[tex]\hat{\vec{L}} = \vec{r} \times \hat{\vec{p}}[/tex]

[tex]\times[/tex] is the cross product...

Do the math and then see if they commute

ps
[px , py] = [px , pz] = 0
 

1. What is the difference between linear momentum operator and angular momentum operator?

The linear momentum operator represents the momentum of a particle moving in a straight line, while the angular momentum operator represents the rotational momentum of a particle about a fixed point.

2. How are the linear momentum operator and angular momentum operator related?

The angular momentum operator can be expressed as a combination of the linear momentum operator and the position operator. This relationship is known as the commutation relation.

3. Can the linear momentum operator and angular momentum operator be applied to all types of particles?

Yes, the linear momentum operator and angular momentum operator can be applied to all types of particles, including point particles, extended particles, and even systems of particles.

4. What is the significance of the eigenvalues of the linear momentum operator and angular momentum operator?

The eigenvalues of these operators represent the possible values for the momentum and angular momentum of a particle, respectively. They also have physical significance in determining the energy levels and behavior of quantum systems.

5. How are the linear momentum operator and angular momentum operator used in quantum mechanics?

These operators are fundamental to the mathematical formalism of quantum mechanics and are used to describe the behavior and properties of particles at the quantum level, including their position, momentum, and energy.

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