Abstract
A new semiclassical approach to the linear and nonlinear one-dimensional Schrödinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition that yields exact eigenenergies for the harmonic-oscillator and Morse potentials.
- Received 9 November 2000
DOI:https://doi.org/10.1103/PhysRevLett.88.170404
©2002 American Physical Society
