WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit
WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit
An efficient and accurate numerical method is presented for the solution of highly oscillatory differential equations. While standard methods would require a very fine grid to resolve the oscillations, the presented approach uses first an analytic (second order) WKB-type transformation, which filters out the dominant oscillations. The resulting ODE is …