# Ket and Bra with the momentum j,m

Hi there!

I try to understand and to use graphical method in the theory of angular momentum. It is not very difficult to master is fundamentals excepting a few things. The most fundamental is the following.

In literature there is used the fact that Kat and Bra vectors with momentum j,m can be mutually permutated using
<jm| = (-1)j-m |j, -m>. It is clear for integer j. But how to understand this fact, for example, in the case j = 1/2 ?

I'm absolutely novice at forums where scientific questions are discussed. So, first of all, I would be glad to see a few words about where else I can discuss such questions. What cites / forums are the most popular for these purposes?

With Best Regards,
Antony Gorkh.

Related Quantum Physics News on Phys.org
dextercioby
Homework Helper
j-m in the exponential is always an integer. If you take j=3/2, then m has 4 possible values: -3/2, -1/2, 1/2 and 3/2. Evaluate j-m for all 4 possible cases.

j-m in the exponential is always an integer. If you take j=3/2, then m has 4 possible values: -3/2, -1/2, 1/2 and 3/2. Evaluate j-m for all 4 possible cases.
Yes, it's obvious true. But the deal is in the other thing.

In the case of integer j every state |jm> is represented by spherical function, and the formula above is just a property of spherical functions. But in the case of semi-integer j we have the other picture. For example in the case of 1/2 |jm> is a column of 2 elements in the basis (1,0)T, (0,1)T, and it's hard to understand how that formula can still hold. But it is so (in some magic way) and it is used widely in literature.

I used the book "Graphical method of spin algebras" by E. Elbaz and B. Castel. The formula (1.2.5) chapter 1, paragraph 2. I use Russian edition, so there may be some shift.

Last edited:
dextercioby