Magnetic field effects on the quantum wire energy spectrum and Green's function

We analyze the energy spectrum and propagation of electrons in a quantum wire on a 2D host medium in a normal magnetic field, representing the wire by a 1D Dirac delta function potential which would support just a single subband state in the absence of the magnetic field. The associated Schrödinger Green's function for the quantum wire is derived in closed form in terms of known functions and the Landau quantized subband energy spectrum is examined.