Related papers: Energy Level Sets for the Morse Potential
Based on a functional-integral formalism, a generalization of the self-energy-functional theory (SFT) is proposed which is applicable to systems of interacting electrons with disorder. Similar to the pure case without disorder, a…
We show that the numerical results contained in a recent paper are affected by a non optimal implementation of the methods which have been used to obtain these results. A careful analysis done using the Rayleigh-Ritz method provides a…
This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound states energy spectrum by diagonalizing the finite…
A new way for obtaining the bound-states for arbitrary non zero l-states of the rotating Morse potential is presented. We show that by making use of the inverse contour representation, which is based on a knowledge of the integral…
We analyze and clarify how the SGA (spectrum generating algebra) method has been applied to different potentials. We emphasize that each energy level $E_\nu$ obtained originally by Morse belongs to a {\em different} ${\mathfrak {so}}(2,1)$…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
Due to one of the most representative contributions to the energy in diatomic molecules being the vibrational, we consider the generalized Morse potential (GMP) as one of the typical potential of interaction for one-dimensional microscopic…
The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent…
We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter $\lambda $. The ground state can be obtained exactly and its energy…
This article addresses a number of issues associated with the problem of calculating contributions from the electromagnetic quantum induced energy and stress in a stationary material with an inhomogeneous polarizability. After briefly…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
It is well-known that a numerical method which is at the same time geometric structure-preserving and physical property-preserving cannot exist in general for Hamiltonian partial differential equations. In this paper, we present a novel…
An octopus program is demonstrated to generate electron energy levels in three-dimensional geometrical potential wells. The wells are modeled to have shapes similar to cone, pyramid and truncated-pyramid. To simulate the electron energy…
We present perturbative energy eigenvalues (up to second order) of Coulomb- and harmonic oscillator-type fields within a perturbation scheme. We have the required unperturbed eigenvalues ($E_{n}^{(0)}$) analytically obtained by using…
The effects of kinetic-energy preservation errors due to Runge-Kutta (RK) temporal integrators have been analyzed for the case of large-eddy simulations of incompressible turbulent channel flow. Simulations have been run using the…
Recent advances in many-body physics have made it possible to study correlated electron systems at the two-particle level. In Dynamical Mean-Field theory, it has been shown that the metal-insulator phase diagram is closely related to the…
A focus of recent research in quantum computing has been on developing quantum algorithms for differential equations solving using variational methods on near-term quantum devices. A promising approach involves variational algorithms, which…
Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated…
The off-resonant hyperpolarizability is calculated using the dipole-free sum-over-stats expression from a randomly chosen set of energies and transition dipole moments that are forced to be consistent with the sum rules. The process is…