Total angular momentum of N identical bosons

In summary: This is due to the permutation symmetry of identical bosons and the Clebsch-Gordan coefficients. In summary, the allowed values of the total angular momentum quantum number for N spin-1 bosons on the same spatial orbit are s=0,2,4,...,N if N is even, and s=1,3,5,...,N if N is odd, due to the permutation symmetry and Clebsch-Gordan coefficients.
  • #1
wdlang
307
0
assume that we have N spin-1 bosons all on the same spatial orbit.

The problem is that what values the total angular momentum can be?

I am puzzled by this problem for a long time

maybe a bit permutation group theory is needed?

i guess this type of problem is well solved

Is there any book i can consult?
 
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  • #3
malawi_glenn said:
You already asked this

https://www.physicsforums.com/showthread.php?t=318451

Define "spatial orbit", you mean they have same L?


You can have

max|J_1 + J_2 + .. J_N | > J_tot > min|J_1 + J_2 + .. J_N |

where J_i = S_i + L_i is vector.

the problem is not so simple

we now treat identical bosons, so the permutation symmetry has to be taken into account
 
  • #4
that is another question, you asked what the specified angular momentum values was, and that is just clebsh gordon table.

Now you want an entire wave function or what?

Can you answer my question what "spatial orbit" refers, otherwise you will gain no help.

a spatial wf has parity (-1)^L

so if you want a symmetric total wf you must consider only the symmetric, or the antisymmetric spin wf's
 
  • #5
malawi_glenn said:
that is another question, you asked what the specified angular momentum values was, and that is just clebsh gordon table.

Now you want an entire wave function or what?

Can you answer my question what "spatial orbit" refers, otherwise you will gain no help.

a spatial wf has parity (-1)^L

so if you want a symmetric total wf you must consider only the symmetric, or the antisymmetric spin wf's

okay,assume that all the bosons are in the s wave orbit
 
  • #6
If they are truly identical (no internal quantum numbers), you can have at most 3 with the same spatial wavefunction, with L_z equal to -1, 0, and 1.

If they are not identical, each boson can have any L_z between -1 and 1.

In each case, total momentum depends on specific values of L_z.
 
  • #7

What is total angular momentum?

Total angular momentum is a physical quantity that represents the combined rotational motion of a system. It is a vector quantity that takes into account both the magnitude and direction of the rotation.

How is total angular momentum calculated?

The total angular momentum of a system can be calculated by adding together the individual angular momenta of all the components of the system. In the case of N identical bosons, this would involve adding together the angular momenta of each boson.

What is the significance of identical bosons in total angular momentum?

Identical bosons, also known as bosonic particles, have the property of being able to occupy the same quantum state. This means that when calculating the total angular momentum of a system of N identical bosons, we must take into account the possibility of the particles occupying the same angular momentum state.

What is the relationship between total angular momentum and spin?

Spin is a type of angular momentum that is intrinsic to particles, meaning it does not arise from their physical rotation. In the case of N identical bosons, the total angular momentum of the system will include both the orbital angular momentum (from the physical rotation) and the spin angular momentum (intrinsic to the particles).

How does total angular momentum affect the behavior of N identical bosons?

The total angular momentum of a system of N identical bosons can have a significant impact on their behavior. For example, it can determine the energy levels and transitions of the system, as well as the types of interactions that can occur between the particles.

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