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

Consider a system A consisting of a spin 1/2 having magnetic moment ##\mu_0##,

and another system A' consisting of 3 spins 1/2 each having magnetic moment ##\mu_0##.

Both systems are located in the same magnetic field B .

The systems are placed in contact with each other so that they are free to exchange energy.

Suppose that, when the moment of A points up (i.e., when A is in its + state), two o f the

moments o f A' point up and one of them points down.

Count the total number of states accessible to the combined system A + A ' w hen the moment o f A points up, and when it points down. Hence calculate the ratio P_/P+, where

P_ is the probability that the moment of A points down and P+ is the probability that it points up.

Assume that the total system A + A ' is isolated.

2. Relevant equations

Basic statistics.

3. The attempt at a solution

I feel like my answer this this is waaaay off just because the way I'm thinking about this makes it seem too easy.

Itfeelslike the probability for A's moment to be + is 3/4, as just from reading previous examples in the book all they seem to note is that it would be the number of + spins over the total number of spins. The - probability would be similar.

What's telling me something is wrong about this is when I generalize to N number of spins in A', I don't get answers that seem right when using this logic.

Is it really this easy or am I missing something???

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# Homework Help: Probabilities for two spin systems interacting in isolation

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