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Lets say we have an atom with an electron that have a spin. That spin can only pointing in 2 directions, in [itex] s_1=\hbar*1/2[/itex] and [itex] s_1=-\hbar*1/2[/itex] and therefore the magnetic moment of an electron is pointing on the opposite site. My Problem here is appearing when whe apply an magnetic field:

From experimental observation you know that the magnetic moment of a whole probe is going to be parallel to the external field, when its stron enough. Why is there such a thing? the direction of the Moment of a Spin is quantized and cant point in the direction of an external field, that is random applied in the room.

thanks for helping