Computing energy eigenvalues of anharmonic oscillators using the double exponential sinc collocation method

DOI10.1016/j.aop.2015.05.026zbMath1360.65197arXiv1411.2089OpenAlexW2962976943MaRDI QIDQ527758

Philippe J. Gaudreau, Hassan Safouhi, Richard Mikael Slevinsky

Publication date: 12 May 2017

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.2089

zbMATH Keywords

asymptotic expansionWKB theoryquantum anharmonic oscillatoranharmonic oscillatorsdouble exponential transformationsinc collocation methodmultiple-well potentialstime independent Schrödinger equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Stability and convergence of numerical methods for ordinary differential equations (65L20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (13)

High energy asymptotics for the perturbed anharmonic oscillator ⋮ The foundations of spectral computations via the solvability complexity index hierarchy ⋮ Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function ⋮ Semiclassical approach of Lorentz symmetry breaking effects at a low energy scenario ⋮ On the computation of eigenvalues of the anharmonic Coulombic potential ⋮ Development of the perturbation theory using polynomial solutions ⋮ A new spectral Galerkin method for solving the two dimensional hyperbolic telegraph equation ⋮ Computing energy eigenvalues of anharmonic oscillators using the double exponential sinc collocation method ⋮ The impact of two transformations on the solutions of second kind Fredholm integral equations system ⋮ Maxwell duality and semiclassical analysis of the interaction of the magnetic quadrupole moment of a neutral particle with external fields ⋮ Semiclassical analysis of the interaction of the magnetic quadrupole moment of a neutral particle with axial electric fields in a uniformly rotating frame ⋮ On symmetrizing the ultraspherical spectral method for self-adjoint problems ⋮ Computation of energy eigenvalues of the anharmonic Coulombic potential with irregular singularities

Uses Software

• LAPACK
• Julia
• GitHub

Cites Work

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• Computing energy eigenvalues of anharmonic oscillators using the double exponential sinc collocation method
• A formal approach to weak and strong coupling expansions and its application to the quantum anharmonic oscillator
• Resurgence of the Euler-Maclaurin summation formula
• The asymptotic iteration method for the eigenenergies of the anharmonic oscillator potential \(V(x)=Ax^{2\alpha} +Bx^2\)
• The independent derivations by Leonhard Euler and Colin MacLaurin of the Euler-MacLaurin summation formula
• Double exponential formulas for numerical integration
• A high-precision study of anharmonic-oscillator spectra
• A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator
• Optimality of the double exponential formula -- functional analysis approach
• Analytic solutions of the Schrödinger equation for the modified quartic oscillator
• Recent developments of the Sinc numerical methods.
• Summary of Sinc numerical methods
• Sinc-Galerkin method for solving nonlinear boundary-value problems
• Renormalized perturbation theory for quartic anharmonic oscillator
• Sinc Function computation of the eigenvalues of Sturm-Liouville problems
• Exponential polynomials
• Comparative study of quantum anharmonic potentials
• Anharmonic oscillator and double-well potential: Approximating eigenfunctions
• An Elementary View of Euler's Summation Formula
• The double exponential sinc collocation method for singular Sturm-Liouville problems
• A unified treatment of Schrodinger's equation for anharmonic and double well potentials
• Function classes for successful DE-Sinc approximations
• On the μx²+ λx⁴interaction
• Numerical implementation of the Sinc-Galerkin method for second-order hyperbolic equations
• DOUBLE WELL POTENTIAL: PERTURBATION THEORY, TUNNELING, WKB (BEYOND INSTANTONS)
• Symmetrization of the Sinc-Galerkin Method for Boundary Value Problems
• Eigenvalues from the Riccati equation
• The Hill determinant method in application to the sextic oscillator: limitations and improvement
• LAPACK Users' Guide
• Numerical Methods Based on Whittaker Cardinal, or Sinc Functions
• The Sinc-Galerkin Method for Fourth-Order Differential Equations
• Energy spectrum of the potential V=ax²+x⁴
• A "Sinc-Galerkin" Method of Solution of Boundary Value Problems
• The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
• The Wentzel-Brillouin-Kramers Method of Solving the Wave Equation
• Open perturbation and the Riccati equation: Algebraic determination of the quartic anharmonic oscillator energies and eigenfunctions
• Failure of the Hill determinant method for the sextic anharmonic oscillator
• On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions
• Sinc-Galerkin method for solving linear sixth-order boundary-value problems
• On the improvement of convergence of Hill determinants
• A sinc-collocation method for initial value problems
• The double-exponential transformation in numerical analysis
• A new asymptotic energy expansion method

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