Two nanowires coupled together such that one has only spin-orbit coupling and the other have Spin-orbit coupling and magnetism; reflection, and transmission of an electron occurs their interface. In the absence of the barrier strength z, reflection would not be possible and the electron will be maximally transmitted. However, when the chemical potential in the right region was greater than that of the left region, it acted as a small barrier, and allowed for small reflection at low energy. This reflection became insignificant at higher energy. Transmission of an electron reduced as z increased while reflection increased, but as the energy of the electron increased, transmission increased while reflection reduced to minimal. In the N1-N2-N3 junctions, N2 acts as a barrier and causes spin-up reflection even when z = 0. On introducing the barrier z, N2-induced spin-up reflection occurs but reduces to minimum value as the energy of the electron increases, and then a barrier-induced spin-up reflection occurs, and keeps increasing to a steady value. During the second stage of spin-up reflection, increasing the energy energizes the reflection process. The tunneling conductance decreased with increasing barrier strength in both trivial and non-trivial phases. In the N1-N2-N3 junctions, when the length of the central wire, L = 1.0, the tunneling conductance could quickly attain maximum values as the energy of the electron increased in both phases unlike when L = 0. The zero-bias conductance abruptly jumped from G (0) = 0 in the trivial regime to G (0) = 1 in the non-trivial regime.

Keywords : Nanowire, Spin, Helical, Eigenvalues, Hamiltonian and Chemical potential.