Related papers: Scattering and bound states by localized potential…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum…
This paper presents an accurate highly efficient method for solving the bound states in the one-dimensional Schr\"odinger equation with an arbitrary potential. We show that the bound state energies of a general potential well can be…
The resulting stationary states and scattering properties of an effective potential brought about by embedding a quantum well in another well are investigated in this work. The composite well system is constructed via a superposition of…
We study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications.
Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
We study the quantum tunnelling of a very complex object of which only part is coupled to an external potential ( the potential barrier ). We treat this problem as the tunnelling of a particle (part of the system affected by the potential)…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
We propose a framework for calculating scattering and bound state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the…
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition…
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
An upgraded concept of solvability of Schr\"{o}dinger-type equations is proposed. In a broader methodical context of non-perturbative quantum theory the innovation involves potentials which are piece-wise analytic yielding differential…