Abstract We solve analytically the Lippmann–Schwinger equation for a linear potential. As an application of this result we investigate the two-dimensional scattering of a scalar particle by a linear potential and by an arbitrary barrier modeled as a boundary-wall.
The Lippmann-Schwinger equation is one of the most important concepts to understand a scattering process in quantum physics. The applications are extended to solid-state physics, atomic and molecular physics, engineering and even in current fields such as quantum wires. In this study we have applied the Lippmann-Schwinger equation to an Envelope- Modulated Sinusoidal Potential. These types of potentials are used actively in fields such as seismology, and various other fields in engineering. Here we have shown that Envelope- Modulated Sinusoidal Potential through the Lippmann-Schwinger equation can be a very important tool.
Abstract In this paper, we propose a pedagogical presentation of the Lippmann–Schwinger equation as a powerful tool, so as to obtain important scattering information. In particular, we consider a one-dimensional system with a Schrödinger-type free Hamiltonian decorated with a sequence of N attractive Dirac delta interactions. We first write the Lippmann–Schwinger equation for the system and then solve it explicitly in terms of an N × N matrix. Then, we discuss the reflection and the transmission coefficients for an arbitrary number of centres and study the threshold anomaly for the N = 2 and N = 4 cases. We also study further features like the quantum metastable states and resonances, including their corresponding Gamow functions and virtual or antibound states. The use of the Lippmann–Schwinger equation simplifies our analysis enormously and gives exact results for an arbitrary number of Dirac delta potentials.