2000/11/22 by Tadanori Hyouguchi, Hyouguchi, Tadanori, Satoshi Adachi +3
Engineering · Physics and Astronomy · #Condensed Matter (cond-mat) #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #Quantum Mechanics and Non-Hermitian Physics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/0011374
7pages 5figures revtex
arxiv created 2000/11/22 · openalex publication_date 2000/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new semiclassical approach to linear (L) and nonlinear (NL) one-dimensional Schrödinger equation (SE) is presented. Unlike the usual WKB solution, our solution does not diverge at the classical turning point. For LSE, our zeroth-order solution, when expanded in powers of ℏ, agrees with the usual WKB solution. For NLSE, our zeroth-order solution includes quantum corrections to the Thomas-Fermi solution, thereby giving a smoothly decaying wave function into the forbidden region.