def spin_z(particles, index):
    """Generates the spin_z projection operator for a system of
        N=particles and for the selected spin index name. where index=0..N-1"""
    mat = np.zeros((2**particles, 2**particles))

    for i in range(2**particles):
        ispin = btest(i, index)
        if ispin == 1:
            mat[i, i] = 1
        else:
            mat[i, i] = -1
    return 1/2.*mat
Generates the spin_z projection operator for a system of
        N=particles and for the selected spin index name. where index=0..N-1