How to Calculate AM and Energy of Multiplet Levels with Spin Orbit Potential?

In summary, the conversation is about calculating the angular momentum (AM) and energy of a particle with spin = 1/2 and orbital AM quantum number L = 2, under a spin orbit potential V = lamda(L.S). The person is struggling with using the C-G theorem and formula to generate irreducible spaces and basis, and using perturbation theory for nondegenerate energy levels. They receive help from someone named Daniel and express gratitude.
  • #1
truth_hunter
7
0
How can I calculate the AM and energy of each level in a resulting multiplet of a particle of spin=1/2 with orbital AM quantum number, L=2 subject to a spin orbit potential,
V=lamda(L.S)?
i am at my wits end! :cry: :cry: :cry:
 
Physics news on Phys.org
  • #2
Well,technically

[tex] \hat{\vec{J}}=\hat{\vec{L}}+\hat{\vec{S}} [/tex]

Use the C-G theorem to generate the irreducible spaces and the C-G formula to find the basis in such spaces.
Then,once u got the basis,then,using perturbation theory for a nondegenerate energy level

[tex] \Delta E^{(1)} =\langle n,j,m_{j} |\hat{V}|n,j,m_{j}\rangle [/tex]

Daniel.
 
  • #3
Cheers mate, I can do it now.
Thanks
 

1. What is a central potential problem?

A central potential problem is a type of problem in physics that involves finding the motion of a particle under the influence of a central force, such as gravity or electrostatic force.

2. What are some examples of central potential problems?

Some examples of central potential problems include the motion of planets around the sun, the motion of electrons around an atomic nucleus, and the motion of objects in a circular orbit due to frictionless surfaces.

3. How is a central potential problem solved?

A central potential problem is typically solved using mathematical equations, such as Newton's laws of motion or the law of universal gravitation. These equations can be used to determine the position, velocity, and acceleration of the particle at any given time.

4. What is the significance of central potential problems in physics?

Central potential problems are important in physics because they help us understand the behavior of objects under the influence of central forces. They are also used in many real-world applications, such as predicting the orbits of satellites and spacecraft.

5. Are there any limitations to solving central potential problems?

Yes, there are some limitations to solving central potential problems. These problems assume that the central force is the only force acting on the particle, which is not always the case in real-world situations. Additionally, they often do not take into account factors such as air resistance or the non-uniform mass distribution of objects, which can affect the accuracy of the solutions.

Similar threads

Replies
1
Views
701
  • Quantum Physics
Replies
21
Views
2K
Replies
2
Views
695
  • Quantum Physics
Replies
12
Views
1K
Replies
18
Views
1K
  • Quantum Physics
Replies
7
Views
1K
Replies
4
Views
135
  • Quantum Physics
Replies
8
Views
733
Replies
10
Views
1K
  • Quantum Physics
Replies
1
Views
804
Back
Top