Help with spinor (1 Viewer)

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A beam of particles with spin 1/2 are coming out of a polarizer and moving along the x-axis, the spin of the particles points in the positive y direction. A uniform magnetic field is turned on and off over a short distance compared with the wavelength of the particle beam. The field is given by Bz(x)=-Bo if -a<x<0
and Bz(x)=0 otherwise.

I have to write down an expression for the wave function corresponding to stationary states, of particles with spin either parallel or antiparallel to the z-axis.


What I've come up with so far is (Ae^(ikx)+Be^(-ikx))
but I'm actually quite lost in this problem. Could someone please give me a hint how to solve this problem?
 

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