A variable-step Numerov method for the numerical solution of the Schrödinger equation

DOI10.1007/s10910-004-1467-3zbMath1070.81513OpenAlexW2035377053MaRDI QIDQ2485886

Higinio Ramos, Jesus Vigo Aguiar

Publication date: 5 August 2005

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-004-1467-3

zbMATH Keywords

Schrödinger equationvariable stepsizeNumerov method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Computational methods for problems pertaining to quantum theory (81-08) Molecular physics (81V55)

Related Items (11)

An adapted explicit hybrid four-step method for the numerical solution of perturbed oscillators ⋮ A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation ⋮ New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation ⋮ Exponential Fitting method for the time-dependent Schrödinger equation ⋮ A new family of three-stage two-step P-stable multiderivative methods with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation and IVPs with oscillating solutions ⋮ A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation ⋮ Development of the perturbation theory using polynomial solutions ⋮ An efficient optimized adaptive step-size hybrid block method for integrating differential systems ⋮ A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation ⋮ A new approach to solve the Schrodinger equation with an anharmonic sextic potential

Cites Work

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• Practical points concerning the solution of the Schrödinger equation
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• On finite difference methods for the solution of the Schrödinger equation
• A family of P-stable eighth algebraic order methods with exponential fitting facilities
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