Abstract
A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained. The convergence rate of the LBRCM for solving the Schrodinger equation is proved from the convergence rate of linear barycentric rational interpolation. Finally, a numerical example verifies the correctness of the theoretical analysis.
Highlights
Schrodinger equation (SDE) is widely used in atomic physics, nuclear physics and solid physics, quantum mechanics, and so on
SDE is only applicable to nonrelativistic particles with low velocity, and there is no description of particle spin
We are concerned with solving the numerical solution of the SDE: zφ(x, t) h2 z2φ(x, t)
Summary
Schrodinger equation (SDE) is widely used in atomic physics, nuclear physics and solid physics, quantum mechanics, and so on. We are concerned with solving the numerical solution of the SDE: zφ(x, t) h2 z2φ(x, t) ih zt. In [4], high-order multiscale discontinuous Galerkin method for one-dimensional stationary SDEs with oscillating solutions is presented. In [5], sixth-order nonlinear SDE is concerned by factorization formula and an analytical method. In [6], nonlinear SDEs are solved by the iterative method. In [13, 14], the linear barycentric rational collocation method (LBRCM) have been used to solve the integro-differential equation. A LBRCM for solving SDE is proposed. E convergence rate of the LBRC method for Journal of Mathematics solving the telegraph equation is proved from the convergence rate of linear barycentric rational interpolation (LBRI).
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