 #1
tanaygupta2000
 204
 14
 Homework Statement:

Enumerate the number of independent ways in which 2N spin1/2's can be com
bined to form a total spin1. Here, N is an integer.
 Relevant Equations:

Addition of spins, s1 + s2 = S
s1 = s2 = 1/2
To the extent I understood this question, we have to enumerate the total no. of ways to get a total of spin S = 1 from 2N number of spin1/2's.
Now, I think that by spin1/2's, the question is referring to s1 = s2 = 1/2 (and not something like 3/2, 5/2, ...).
When N = 1, we have 1/2 + 1/2 => No. of ways = 1
When N = 2, we have 1/2 + 1/2 + 1/2 + 1/2 => No. of ways = 3 + 2 + 1 = 6
Likewise,
For N = N, No. of ways should be given by = (2N1)+(2N2)+(2N3)+...+3+2+1
I am sure I'm missing many things here, this question carries 15 marks.
Kindly help !
Now, I think that by spin1/2's, the question is referring to s1 = s2 = 1/2 (and not something like 3/2, 5/2, ...).
When N = 1, we have 1/2 + 1/2 => No. of ways = 1
When N = 2, we have 1/2 + 1/2 + 1/2 + 1/2 => No. of ways = 3 + 2 + 1 = 6
Likewise,
For N = N, No. of ways should be given by = (2N1)+(2N2)+(2N3)+...+3+2+1
I am sure I'm missing many things here, this question carries 15 marks.
Kindly help !