New analytic solution of Schrödinger's equation

¹  Institute for Quantum Studies and Department of Physics, Texas A&M University - College Station, TX, USA
²  Applied Physics and Materials Science Group, Princeton University - Princeton, NJ, USA
³  Department of Physics, University of North Texas - Denton, TX, USA

Received: 17 January 2010
Accepted: 18 February 2010

Abstract

We obtain an analytic solution beyond adiabatic approximation by transferring the 1D Schrödinger equation into the Ricatti equation. Then we show that our solution is more accurate than JWKB approximation. The generalizations of the approach to 3D are suggested, and possible applications of obtained solutions are discussed.