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While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…

Numerical Analysis · Mathematics 2017-05-09 Pankaj K Mishra , Sankar K Nath , Gregor Kosec , Mrinal K Sen

We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…

Quantum Physics · Physics 2019-04-19 Amlan K. Roy

Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a…

Quantum Physics · Physics 2013-07-15 Amlan K. Roy

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $\Phi$,…

Numerical Analysis · Mathematics 2026-05-28 Bastien Grosse

We investigate a Dirac-type equation in (2+1) dimensions modified by Lifshitz spatial derivatives with dynamical exponent $z=2$, focusing on the spectral properties of bound states under radial confinement. Analytical solutions are obtained…

Strongly Correlated Electrons · Physics 2026-05-12 Lucas K. R. Queiroz , Van Sérgio Alves , Nilberto Bezerra , Luis Fernández , Francisco Peña

In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied…

Numerical Analysis · Mathematics 2024-05-08 Liu Liu , Kunlun Qi

The stochastic inverse eigenvalue problem aims to reconstruct a stochastic matrix from its spectrum. While there exists a large literature on the existence of solutions for special settings, there are only few numerical solution methods…

Numerical Analysis · Mathematics 2020-04-17 Gabriele Steidl , Maximilian Winkler

We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…

Mathematical Physics · Physics 2026-05-28 Owen Sutton , Alexander B. Watson

Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…

Numerical Analysis · Mathematics 2020-09-23 Clark A. Pennie , Irene M. Gamba

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…

Quantum Physics · Physics 2014-10-01 J. A. Sanchez-Monroy , C. J. Quimbay

The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…

Quantum Physics · Physics 2008-08-08 Sameer M. Ikhdair , Ramazan Sever

The achievement of spectral super-resolution sensing is critically important for a variety of applications, such as radar, remote sensing, and wireless communication. However, in compressed spectrum sensing, challenges such as spectrum…

Information Theory · Computer Science 2026-04-30 Baoguo Liu , Huiguang Zhang , Wei Feng , Zongyao Liu , Zhen Zhang , Yanxu Liu

In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…

High Energy Physics - Theory · Physics 2019-04-18 Ozlem Yesiltas

Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry,…

Mathematical Physics · Physics 2010-03-05 Altug Arda , Ramazan Sever , Cevdet Tezcan

We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…

Mathematical Physics · Physics 2009-11-11 Hakan Ciftci , Richard L. Hall , Nasser Saad

We present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase space procedures; the…

Mathematical Physics · Physics 2008-11-26 J M Pons , D C Salisbury , L C Shepley

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…

Mathematical Physics · Physics 2015-06-22 Richard L Hall , Nasser Saad

Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Lawrence E. Kidder , Lee Samuel Finn

By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin- particle subject to the complex -symmetric scalar and vector P\"oschl-Teller (PT) potentials…

Quantum Physics · Physics 2012-10-05 Sameer M. Ikhdair , Majid Hamzavi

Unlike the situation for the 1d Dirac delta derivative Schrodinger pseudo potential (SPP) and the 2d Dirac delta SPP, where the indeterminacy originates from a lack of scale in the first and both a lack of scale as well as the wave function…

Quantum Physics · Physics 2024-02-08 Michael Maroun