Related papers: Energy spectrum design and potential function engi…
We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
A theoretical scheme for the analysis of experimental data on IR spectroscopy for a quantum particle in a double well potential (DWP) is suggested. The analysis is based on the trigonometric DWP for which the exact analytic solution of the…
Potential energy surfaces of electron dynamics (ePES) are constructed from a model of localized electron wave packets (eWP) with non-orthogonal valence-bond (VB) spin coupling and applied to quantum dynamics simulations of high harmonic…
For quasiexactly solvable (QES) potentials a certain number of wave functions and energy levels can be analytically calculated. The complexity of an explicit calculation of the energy levels grows with the dimension of the QES sector. For a…
Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. It consists of a four-parameter polynomial with continuous spectrum on the whole real line…
We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis…
A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
It is shown that Schr\"odinger equation with combination of three potentials U = - {\alpha} r^{-1} + {\beta} r + kr^{2}, Coulomb, linear and harmonic, the potential often used to describe quarkonium, is reduced to a bi-confluent Heun…
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy…
A new scheme for constructing approximate effective electron potentials within density-functional theory is proposed. The scheme consists of calculating the effective potential for a series of reference systems, and then using these…
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is optimal with respect to a large class of potential functions…
We have developed a new simple method to build the exact analytical expression of the eigenenergy as a function of the potential. The idea of our method is mainly based on the partitioning of the potential curve, solving the Schr\"odinger…
A benchmark-quality potential energy curve is reported for the H$_3$ system in collinear nuclear configurations. The electronic Schr\"odinger equation is solved using explicitly correlated Gaussian (ECG) basis functions using an optimized…
We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases…
The optimized effective potential (OEP) approach has so far mainly been used in benchmark studies and for the evaluation of band gaps. In this work, we extend the application of the OEP by determining the analytical ionic forces within the…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
A class {\cal R}_p of purely bosonic models is characterized having the following properties in the Bargmann Hilbert space of analytic functions: (i) wave function \psi(\epsilon,z)=\sum_{n=0}^\infty \phi_n(\epsilon) z^n is the {\em…