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

For a magnetic particle with an angular momentum "quantum number", j, the allowed values of the z component of a particles magnetic moment are:

µ = -jδ, (-j + 1)δ, ..., (j-1)δ, jδ

δ is a constant, and j is a multiple of 1/2

Show that the partition function of a single magnetic particle is

Z = sinh[βδB(j+1/2)] / sinh[(βδB)/2]

2. Relevant equations

in general, Z = Σ exp(β·E(s))

and for a magnetic particle: E(s) = -µB

1 + x + x^{2}+ .... +x^{n}= 1 - x^{n+1}/ 1 - x

3. The attempt at a solution

If i did things correctly, I can get to an equation:

Z = [1 - exp(-βδB(j+1/2))] / [1 - exp(-βδB/2)]

I got this just by x = exp(-βδB/2) and noticing that the n in the finite sum is 2j. (if you add j to all µ to get a sequence from 0 to 2j instead of -j to j). Then I plugged into the mathematical identity I have above. The problem is converting this in to the sinh term that the question asks for. Unless of course, it is completely wrong, in which case I'm rather lost on the subject.

Thanks for teh help in advance,

M@

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Partition Function of a Single Magnetic Particle

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