I am reading an article on Arxiv about modelling the electron structure in a nanowire crystal: http://arxiv.org/abs/1511.08044 But I am having trouble understanding the hamiltonians (1) and (2). In (1) what is the purpose of the term E_gap/2. Is that just a reference point for the energy or something? In (2) why does the spin orbit term look like it does? In my world spin orbit is something like S⋅L, i.e. a coupling between the orbital angular momentum of the nucleus and the spin of the electrons. Is that what the terms describes?