相关论文: Vibrational Levels of a Generalized Morse Potentia…

Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in…

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…

We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential…

We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schr\"odinger equation with the Laplace…

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…

While dealing with the J-Matrix method for the harmonic oscillator to write down its tridiagonal matrix representation in an orthonormal basis of L2(R); we rederive a set of generalized coherent states (GCS) of Perelomov type labeled by…

The generalized moment problem (GMP) is an infinite dimensional linear problem over the cone of finite nonnegative Borel measures. When a GMP instance involves finitely many polynomial moment constraints, moment/sum-of-squares hierarchies…

We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment…

An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…

The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…

The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis,…

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse…

We solve the wave equation for gravitational waves emitted by compact objects systems using the Multipolar Post-Minkowskian (MPM) method, and in the presence of Lorentz invariance violating terms. We select a Lorentz-violating extension of…

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

Molecular dynamics simulations are an invaluable tool in numerous scientific fields. However, the ubiquitous classical force fields cannot describe reactive systems, and quantum molecular dynamics are too computationally demanding to treat…

We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…

As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm…

We introduce an $hp$-version symmetric interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the biharmonic equation on general computational meshes consisting of polygonal/polyhedral…

A near-field motion parameter estimation method is proposed. In contract to far-field sensing systems, the near-field sensing system leverages spherical-wave characteristics to enable full-vector location and velocity estimation. Despite…

Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very…