Spin Transition, how made it?

[DavidD]

How made spin transition from 1/2 to -1/2 or visa versa? And how it need make if electron is withouth nuclear and if electron is around nuclear? And how prepere spin in state 1/2 or -1/2?

[Bareil]

you mean you are interested in the details of the transition process? First, you have a spectrum of two base states, |+1/2> and |-1/2>. This is a fundamental fact, you cannot derive it from more fundamental principles in current quantum theory. Now, if you wanna regard the transition process, your electron has a state that is a superposition of both base states:

|psi> = a |+1/2> + b |-1/2>

where |a|^2 + |b|^2 = 1. The process starts with |a|=1, b=0. With time passing, amplitude |a| is decreasing and |b| increasing. Finally, it develops to a=0 and |b|=1. For this transition, you need some Hamiltonian to induce it, for example, interaction Hamiltonian of electron's magnetic dipol momentum and external magnetic field.

It does not matter whether electron is bound to atom or not.

To prepare electrons in desired state, you can take a couple of electrons and shoot them through some apparatus that induces inhomogenuous magnetic field, so that electrons with spin-up go to the one exit and those with spin-down to ethe other exit. At the first exit, you can collect you spin-up electrons.