Total angular momentum of N identical bosons

[wdlang]

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?

 

[malawi_glenn]

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.

 

[wdlang]

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

 

[malawi_glenn]

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

 

[wdlang]

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

 

[hamster143]

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.

 

[Avodyne]

I gave a complete answer to this in your other thread:
https://www.physicsforums.com/showthread.php?t=318451
The short answer is the allowed values of the total angular momentum quantum number are s=0,2,4,...,N if N is even, and s=1,3,5,...,N if N is odd.