(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the no. of energy levels with different values of total spin for a system of N particles with spin 1/2

3. The attempt at a solution

Let f be the no. ways to get a z projection of spin, then

[itex]f(\sigma )=Binomial(N,\frac{1}{2}N + \sigma)[/itex]

Where Binomial(a,b) is a chose b

That part makes perfect sense

To each energy level with a given S there corresponds 2S+1 states with σ=S...-S

Again, I know this

Hence it is easy to see that the no. different energy levels with a given value of S are

n(S)=f(s)-f(s+1)

And that is where it lost me, I don't understand why this is and I feel like I'm missing something simple..

Could anyone offer any help?

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# Missing something pretty simple in counting energy levels?

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