Related papers: Variable-phase method and Levinson's theorem in tw…
It is known that the variational methods are the most powerful tool for studying the Coulomb three-body bound state problem. However, they often suffer from loss of stability when the number of basis functions increases. This problem can be…
We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in…
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The…
Quantum-logic techniques used to manipulate quantum systems are now increasingly being applied to molecules. Previous experiments on single trapped diatomic species have enabled state detection with excellent fidelities and highly precise…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
We investigate the effect of long-range Coulomb interaction on the two-electron scattering in the integer quantum Hall regime at bulk filling factor 2. A parallel version of the Split-Step Fourier method evolves the exact two-particle wave…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…
The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a…
n a recent paper we proposed the expansion of the space of variations in energy calculations by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For the…
Traditional mean-field theory is a simple generic approach for understanding various phases. But that approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the…
We present a method enabling us to write in relativistic manner the wave function of some particular two particle bound state models in quantum mechanics. The idea is to expand the bound state wave function in terms of free states and to…
The screened Coulomb potential plays a crucial role in the binding energies of excitons in a thin dielectric slab. The asymptotic behavior of this potential is studied when the thickness of the slab is very small as compared to the exciton…
We show that two-mode squeezed vacuum-like states may be engineered in the Bohm-Madelung formalism by adequately choosing the phase of the wavefunction. The difference between our wavefunction and the one of the squeezed vacuum states is…
We apply the Hulth\`en-Kohn method suggested by V. D. Efros [Phys. Rev. C 99, 034620 (2019)] for calculating various observables in the continuum and discrete spectrum using two-body interactions in single- and coupled-channel systems. This…