# Angular momentum - integer or half-integer

1. Jan 24, 2010

### paweld

Let J be total angular momentum, L - orbital angular momentum and S - intristic momentum (spin). Squares of these operators have appropriate eigenvalues j(j+1), l(l+1), s(s+1). Which of these numbers j,l,s should be integer. I know that spin can have half-integer values. But probably orbital or total momentum values should be integer. Thanks for answer.

2. Jan 24, 2010

### Maxim Zh

The orbital momentum value must be integer. It results from the wave function one-valuedness.
The total momentum value can be half-integer.

3. Jan 24, 2010

### Fredrik

Staff Emeritus
j and s can both be half integer. j is one of the numbers that labels a particle species. The s of a specific particle can only change by integer amounts, and since the lowest possible value of s is always -j and the highest always +j, this means that j must be integer or half integer.

Examples: When j=1, s can take the values -1,0,1. When j=1/2, s can take the values -1/2,1/2.