What Are the Allowed Values of m_n in Angular Momentum?

In summary, the conversation discusses help with solving a homework problem involving angular momentum. The problem involves determining the probability of finding a particle in a specific eigenstate of an operator. The operators J^2, J_z, and K(hat) are mentioned, along with the spherical polar angles and the state |j,m>. The conversation also includes a discussion about the allowed values of m_n and the different approaches to solving the problem.
  • #1
fizixgal
1
0
Need help with angular momentum!

Hi - I have been working on this homework problem for 3 days now and I'm so stumped! Any help would be much appreciated! :blushing:

A particles with total angular momentum J = 1 is in an eigenstate |j,m> of the operators J^2, J_z. This problem concerns the probability of finding the particle in an eigenstate |j,m_n> of the operator K(hat) = n (dot) J which is the projection of ang. mom. along n.

n = sin(theta)cos(phi) e_x + sin(theta)sin(phi) e_y + cos(theta) e_z ---> spherical polar angles

What are allowed values of m_n?

How would I go about finding the probability of finding the particle in eigenstate |j,m_n> for any value of m_n when the particle is prepared in the state |j,m=1> where I think j is always 1 for this problem.

Thanx!
 
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  • #2
What do you think the allowed values of [tex]m_n[/tex] are? Is there anything particularly sacred about your choice of the z direction?

Also, there are two good ways to look at this problem. One is to compute said rotated operator eigenstates, the other is to rotate the z-direction eigenstate problem into the n-direction. Either way works.
 

FAQ: What Are the Allowed Values of m_n in Angular Momentum?

What is angular momentum?

Angular momentum is a measure of the rotational motion of an object. It is a vector quantity that takes into account the mass, position, and velocity of an object as it rotates around an axis.

How is angular momentum different from linear momentum?

Angular momentum is different from linear momentum in that it takes into account the rotational motion of an object, while linear momentum only considers the linear motion of an object.

What factors affect angular momentum?

The factors that affect angular momentum include the mass of the object, the distance from the axis of rotation, and the velocity of the object. These factors determine how much rotational force an object has.

How is angular momentum conserved?

Angular momentum is conserved, meaning it remains constant, as long as there is no external torque acting on an object. This is known as the law of conservation of angular momentum.

How is angular momentum used in real-world applications?

Angular momentum is used in many real-world applications, such as calculating the stability of rotating objects like satellites and gyroscopes, predicting the motion of planets and galaxies, and studying the behavior of spinning tops and other toys.

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