def METHOD_NAME(backend):
    hc = F.chemical_potential(0.8, 0, 3)
    h1 = FT.get_hmatrix(hc, 3) + 0.4 * tc.backend.eye(2**3)
    # constant shift
    h2 = FT.chemical_potential_jw(0.8, 0, 3)
    np.testing.assert_allclose(h1, h2, atol=1e-5)
    hc = F.hopping(0.8j, 0, 1, 3)
    h1 = FT.get_hmatrix(hc, 3)
    h2 = FT.hopping_jw(0.8j, 0, 1, 3)
    np.testing.assert_allclose(h1, h2, atol=1e-5)
    hc = F.sc_pairing(0.8, 1, 0, 3)
    h1 = FT.get_hmatrix(hc, 3)
    h2 = FT.sc_pairing_jw(0.8, 1, 0, 3)
    np.testing.assert_allclose(h1, h2, atol=1e-5)