Finite Difference Schemes and the Schrodinger Equation
نویسندگان
چکیده
In this paper, we primarily explore numerical solutions to the Quantum 1D Infinite Square Well problem, and the 1D Quantum Scattering problem. We use different finite difference schemes to approximate the second derivative in the 1D Schrodinger’s Equation and linearize the problem. By doing so, we convert the Infinite Well problem to a simple Eigenvalue problem and the Scattering problem to a solution of a system of linear equations. We examine the convergence of the solution to the infinite square well problem for high order stencils, and compare the computed results to an analytic solution. For the scattering problem, we test both first and second order finite difference schemes for boundary conditions, and compare the convergence of these schemes.
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