Nano-wire in a Magnetic Field

We analyze the energy spectrum and propagation of electrons in a quantum wire on a $2D$ host medium in a normal magnetic field. Here, the Hamiltonian term representing the quantum (nano) wire has the form of a one-dimensional Dirac delta function. We derive the associated Schr\"{o}dinger quantum-wire Green's function in closed form. The energy spectrum is then determined by examination of the frequency poles of the Green's function, with Landau-quantization-like splintering of levels.