Study of the transition from resonance to bound states in quantum dots embedded on a nanowire using the $\mathbf{k}\cdot\mathbf{p}$ method

We study the band structure of semiconductor nanowires with quantum dots embedded in them. The band structure is calculated using the Rayleigh-Ritz variational method. We consider quantum dots of two different types, one type is defined by electrostatic potentials applied to the nanowire, while the other one is defined by adding materials with band offsets with respect to the band parameters of the nanowire. We are particularly interested in the appearance of discrete energy levels in the gap between the conduction band and the valence band of the nanostructure, and in the dependence of the energy of these levels with the intensity of a magnetic field applied along the wire. It is shown that several scenarios are possible, being of particular interest the possibility of transforming states of the discrete into resonances and vice versa