Related papers: Bound and Unbound Wave Functions at Short Distance…
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…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
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 study the internal structure of exotic hadrons, especially focusing on the relation between the compositeness and physical observables. Defined as the probability of finding hadronic molecular components in the wave function,…
The theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. It is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can…
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…
We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…
This research focuses on the possibility of the surjective relation between symmetric potential function and its scattering matrix in 1-dimension. The theory bases on the property of wave function symmetry and boundary conditions. This…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with amplitudes small compared to…
We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of…
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…
Theory of scattering by many small bodies is developed under various assumptions concerning the ratio $\frac{a}{d}$, where $a$ is the characteristic dimension of a small body and $d$ is the distance between neighboring bodies $d =…
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting…
We describe a perturbation expansion for the energy and wave function of a weakly bound particle in a short-range potential in one space dimension.
The spherical wave functions of charge-dyon bounded system in a rectangular spherical quantum dot of infinitely and finite height are calculated. The transcendent equations, defining the energy spectra of the systems are obtained. The…