Divergence-free WKB method.
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.
Hyouguchi
Tadanori
T
Department of Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan.
Adachi
Satoshi
S
Ueda
Masahito
M