Quantum Spin up spin down with magnetic field

[mozartkart]

There is an external magnetic field along the positive z direction B = (0,0, B) and the initial spin direction at time t₀= 0 is specified by the direction cosines
Ŝ₀= (cos α₀, cos β₀, cos γ₀)
where α₀, β₀, γ₀ are the angles between the initial spin and the x, y, z axes, respectively.
This initial spin pointing in the direction Ŝ₀ can be represented in terms of spin up and down states along z direction:
ψ(α₀ ,β₀ ,γ₀ ) = A(α₀ ,β₀ ,γ₀ )α + B(α₀ ,β₀ ,γ₀β ) ,
What are A and B?

For the Psi= A alpha + B beta part alpha and beta represent the |+> and |-> z sates respectively.

Hey everyone on this fine night,
I really don't know where to start and was wondering if someone could give me a push in the right direction? Is this just asking what is the probability of it being up or down? I really can't get my foot out of the door on this :(

 

[Nate810]

A and B represent the probabilities of the spin being in the up or down states respectively. The probability of the spin being in an up state is given by A, and the probability of it being in a down state is given by B. To determine these probabilities, you can use the equations A = cos^2(α0) + cos^2(β0) + cos^2(γ0) and B = sin^2(α0) + sin^2(β0) + sin^2(γ0).