Related papers: Alternative quantisation condition for wavepacket …
The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a…
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…
We consider a single impurity atom trapped in a double well (DW) potential created by a dipolar two-soliton molecule in a quasi-one-dimensional geometry. By solving the eigenvalue problem for the impurity atom in the DW potential, we find…
A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite…
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the…
We present an exact quantization condition for the time independent solutions (energy eigenstates) of the one-dimensional Dirac equation with a scalar potential well that gives only two `effective' turning points (defined by the roots of…
We present a comprehensive second quantization scheme for radiative photonic devices. We canonically quantize the continuum of photonic eigenmodes by transforming them into a discrete set of pseudomodes that provide a \textit{complete} and…
The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes and chemical reactions. It is thus a long-standing scientific dream to measure the dynamics of two bound correlated electrons in the…
We compare the classical (mean-field) dynamics with the quantum dynamics of atomic Bose-Einstein condensates in double-well potentials. The quantum dynamics are computed using a simple scheme based upon the Raman-Nath equations. Two…
We apply the extended Nikiforov-Uvarov method to the non-relativistic limit of the Dirac equation with a Coulomb potential in spaces of constant curvature. In this case, the radial equation reduces to the Heun equation, and the extended…
We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with non--symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled…
We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $H=e^{x}+e^{-x}+e^{p}+e^{-p}$ in terms of the refined topological invariants of a local Calabi-Yau geometry has an intimate relation with…
In the second part of this paper in micro canonical ensemble the new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner…
A numerical algorithm based on the probabilistic path integral approach for solving Schroedinger equation has been devised to treat molecular systems without Born-Oppenheimer approximation in the non relativistic limit at zero temperature…
The time-independent nonlinear Schr\"odinger equation is solved for two attractive delta-function shaped potential wells where an imaginary loss term is added in one well, and a gain term of the same size but with opposite sign in the…
In this paper we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Though we focused primarily on the two-dimension physical systems, the method is valid for…
The Schr\"odinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and…
We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest…
We present an analytical method to compute the wavenumbers and electric fields of the space-charge-wave eigenmodes supported by a two-stream electron beam, consisting of a solid inner cylindrical stream and a coaxial outer annular stream,…
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…