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unfortunately, i have still some troubles to understand the concept of spin and wanted to get things right now, so maybe someone of you could help me:

let me start with an electron, which is a spin 1/2 particle and has therefore two possible values for the z-direction of the spin: -h/(4π) and +h/(4π)

does this mean, that the direction in space of the spin is completely arbitrary and only the absolute value of the spin is determined?

i heard that a spin causes a magnetic field. is there anywhere an equation that gives me the magnetic field in terms of a free electron with arbitrary spin?(just for curiousity)

am i correct by saying that only based on the fact that there are two possibles for the z direction, this does not mean, that if you have two electrons with the same spin, that they cause the same magnetic field, as it is impossible to determine the x and y direction of the spin and therefore the contribution of these two directions to the magnetic field? (i guess this would also mean that the answer to my question, if there is a general equation that gives me the magnetic field in terms of the spin, would be that this is not so)

is there are reason that you have an energy yield, when you have positive spin quantum number in z-direction and a homogenous magnetic field in this direction or does this have anything to do with attrative forces between the magnetic field caused by the spin and the magnetic field of the field?

and again i am sorry about my english, i am still practising.

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# Spin and magnetic field

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