def METHOD_NAME(w, z):
    zp = e_ia * z.reshape(e_ia.shape)
    zm = w/e_ia * z.reshape(e_ia.shape)
    x = (zp + zm) * .5
    y = (zp - zm) * .5
    norm = lib.norm(x)**2 - lib.norm(y)**2
    norm = numpy.sqrt(.5/norm)  # normalize to 0.5 for alpha spin
    return (x*norm, y*norm)