- #1
Wan Anavan
- 2
- 1
- Homework Statement
- Analysis of Angular Momentum
- Relevant Equations
- Commutators
is my solution correct?
Last edited:
A Simple angular momentum analysis question (check my solution please)
- Thread starter Wan Anavan
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In summary, the conversation involves a discussion about the correctness of a solution related to the analysis of angular momentum and commutators. The expert advises the other person to be more careful and to write out more steps to avoid making mistakes. The person then confirms that the solution is correct and suggests checking it by working out a specific equation. A humorous comment is made at the end, leading to a brief hijack of the conversation.
is my solution correct?
- #2
BvU
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Not the way you write it. $$[L_x,L_y]=-i\hbar L_z$$
[edit] Sorry for confusing you. I made (a single) a sign error too !
The intention was to write $$[L_x,L_y]=\ \ \ i\hbar L_z\\ \ [L_y,L_x]=-i\hbar L_z$$
Two wrongs doesn't make a right
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- #3
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Wan Anavan said:
You are not being careful enough. You must write out more steps as you're going wrong with the shortcuts.
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- #4
BvU
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No. Write out ##L_+## and ##L_-## and explicitly multiply
- #5
Wan Anavan
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BvU said:
PeroK said:
then the answer is not zero
- #6
BvU
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This time answer and solution are correct.
You can check yourself by working out ##\Bigl [L_+,L_-\Bigr ]##
You can check yourself by working out ##\Bigl [L_+,L_-\Bigr ]##
- #7
berkeman
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[ hijack ]
[ /hijack ]
LOL. Shouldn't that be "Too wrongs doesn't make a right"?BvU said:
[ /hijack ]
FAQ: A Simple angular momentum analysis question (check my solution please)
1. What is angular momentum and how is it calculated?
Angular momentum is a measure of an object's rotational motion. It is calculated by multiplying the object's moment of inertia by its angular velocity.
2. How is angular momentum conserved?
Angular momentum is conserved when there is no external torque acting on a system. This means that the total angular momentum of a system will remain constant unless an external force is applied.
3. Can angular momentum be negative?
Yes, angular momentum can be negative. This occurs when an object's angular velocity is in the opposite direction of its moment of inertia.
4. How does angular momentum relate to linear momentum?
Angular momentum is the rotational equivalent of linear momentum. Just as linear momentum is conserved in a system with no external forces, angular momentum is conserved in a system with no external torque.
5. How can angular momentum be applied in real-life situations?
Angular momentum has many practical applications, including in the fields of physics, engineering, and astronomy. Examples include the spinning of a top, the rotation of a planet around its axis, and the movement of a gyroscope.