A new effective algorithm for the resonant state of a Schrödinger equation

DOI10.1016/j.cpc.2004.12.004zbMath1196.65125OpenAlexW2029286515MaRDI QIDQ709712

Zhongcheng Wang

Publication date: 18 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2004.12.004

zbMATH Keywords

Schrödinger equationP-stabletrigonometric fittingNumerov methodhigh-oscillatory solution

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (9)

Trigonometrically-fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation ⋮ Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ Pseudospectral methods of solution of the Schrödinger equation ⋮ A trigonometrically-fitted one-step method with multi-derivative for the numerical solution to the one-dimensional Schrödinger equation ⋮ P-stable linear symmetric multistep methods for periodic initial-value problems ⋮ Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation ⋮ Trigonometrically-fitted method for a periodic initial value problem with two frequencies ⋮ Satellite-based phase-matching quantum key distribution

Cites Work

• A Mathematica program for the two-step twelfth-order method with multi-derivative for the numerical solution of a one-dimensional Schrödinger equation
• A variable step method for the numerical integration of the one- dimensional Schrödinger equation
• Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
• Two-step methods for the numerical solution of the Schrödinger equation
• An eighth-order formula for the numerical integration of the one- dimensional Schrödinger equation
• P-stable exponentially fitted methods for the numerical integration of the Schrödinger equation
• Embedded methods for the numerical solution of the Schrödinger equation
• Practical points concerning the solution of the Schrödinger equation
• The numerical solution of coupled differential equations arising from the Schrödinger equation
• Symmetric Multistip Methods for Periodic Initial Value Problems
• A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION
• An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields

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