An Adaptive Basis Function for Meshless Simulation of Quantum Wave Packets at Optical Frequencies

In this work, an adaptive and efficient basis function is presented by which the Schrodinger equation can be solved using meshless method in an accurate and fast approach. The base of this achievement is the quantum wave packet. The proposed basis function reduces time consumption of the meshless method, approximately to half. Also, it inherits the fundamental properties of wave packets. Therefore, an accuracy and precision in simulation of wave function is obtained which is higher than some other numerical methods such as conventional meshless method or finite element method (FEM). This precision will be shown in practice by simulating a quantum well laser. Index Terms — Meshless method, basis function, Schrodinger's equation, Gaussian wave packets, Kronecker delta property.