Angular momentum eigenstates and total mom. S?

In summary, when finding the total angular momentum of a spin 2 particle, assuming zero orbital angular momentum, the eigenvalue of the total angular momentum squared is S^2 = s(s+1)*(h-bar)^2, with s = 2. This is similar to the treatment of spin-1/2 particles, where the orbital and spin components of angular momentum are added together. In the case of non-zero orbital angular momentum, the eigenvalue of L^2 is l(l+1)*(h-bar)^2, with j ranging from abs(l-s) to abs(l+s) in integer steps.
  • #1
qqchico
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My problem is with finding total angular momentum S of a spin 2 particles. My quantum book doesn't do any examples with spin 2 particles do i just do
J(J+1)|j,m> and just plug in j and that will be my value.
 
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  • #2
Assuming zero orbital angular momentum, L = 0, then the eigenvalue of the total angular momentum squared is just S^2 = s(s+1)*(h-bar)^2, with s = 2.

Generally, the treatment of the problem is the same as with spin-1/2 particles, so the orbital- and spin-components of angular momentum add together as usual in the case of non-zero orbital angular momentum, ie j goes between abs(l - s) and abs(l+s) in integer steps, then l(l+1)*(h-bar)^2 is the eigenvalue of L^2.

Cheyne
 
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  • #3


Yes, you are correct in your approach. The total angular momentum of a spin 2 particle can be calculated using the formula J(J+1)|j,m>, where J is the spin quantum number and m is the magnetic quantum number. You can simply plug in the appropriate value for J and calculate the total angular momentum. However, it is important to note that the value of J for a spin 2 particle can range from 0 to 2, so you will need to determine the specific value of J for your particle in order to accurately calculate the total angular momentum. Additionally, it may be helpful to consult other sources or textbooks for examples of spin 2 particles to gain a better understanding of the concept.
 

1. What is angular momentum eigenstate?

An angular momentum eigenstate is a state in which the angular momentum of a system has a definite value. This means that the system is in a state of uniform rotation and its angular momentum is quantized, meaning it can only take on certain discrete values.

2. How are angular momentum eigenstates related to total angular momentum?

Angular momentum eigenstates are the basis states for describing the total angular momentum of a system. Any state of a system can be expressed as a linear combination of these eigenstates, with the coefficients representing the probabilities of obtaining specific values of total angular momentum in a measurement.

3. What is the significance of angular momentum eigenstates in quantum mechanics?

Angular momentum eigenstates are important in quantum mechanics because they provide a complete description of the angular momentum of a system. They also obey the laws of quantum mechanics, allowing for precise predictions about the behavior of systems at the atomic and subatomic level.

4. Can angular momentum eigenstates have a non-zero total angular momentum?

Yes, angular momentum eigenstates can have a non-zero total angular momentum. This is because the eigenstates themselves have a definite value of angular momentum, but when combined in a linear combination, they can result in a non-zero total angular momentum.

5. How do angular momentum eigenstates behave under rotations?

Angular momentum eigenstates are invariant under rotations, meaning they do not change when the system is rotated. This is because they are eigenstates of the angular momentum operator, which is a conserved quantity in a rotationally invariant system.

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