Exact Green's function for rectangular potentials and its application to quasi-bound states

Abstract

In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also generalizing and resuming results in the literature. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression. From the poles and residues of the Green's function the bound states eigenenergies and eigenfunctions with the correct normalization constant are obtained. In order to show the versatility of the method, an application of the Green's function approach to extract information of quasi-bound states in rectangular barriers, where the standard analysis of quantum amplitudes fail, is presented.

9 pages, 7 figures, few typos corrected, matches published version

References in corpus (9)

• Observation of the Fano-Kondo Anti-Resonance in a Quantum Wire with a Side-Coupled Quantum Dot
• Dynamics of a Tonks-Girardeau gas released from a hard-wall trap
• Distribution of time-constants for tunneling through a 1D Disordered Chain
• Green functions for generalized point interactions in 1D: A scattering approach
• Quantum chaos with non-periodic, complex orbits in the Resonant Tunneling Diode
• Explanation and observability of diffraction in time
• Tunneling Ionization Rates from Arbitrary Potential Wells
• Green function approach for scattering quantum walks
• Superdiffusivity of quantum walks: A Feynman sum-over-paths description

Cited by in corpus (4)

• Green's function approach for quantum graphs: an overview
• Unitary equivalence between the Green's function and Schrödinger approaches for quantum graphs
• The Quantum Steeplechase
• Exact and quasiclassical Green's functions of two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction in parallel magnetic field