Divergence-free WKB method
Tadanori Hyouguchi, Satoshi Adachi, Masahito Ueda
Abstract
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 , 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.
Create a lesson
Related papers
Knots in Condensed Matters
Y. M. Cho
Bouchaud's model exhibits two different aging regimes in dimension one
Gerard Ben Arous, Jiri Cerny
Periodic diffraction patterns for 1D quasicrystals
Pawel Buczek, Lorenzo Sadun, Janusz Wolny
Adiabatic association of ultracold molecules via magnetic field tunable interactions
Krzysztof Goral, Thorsten Koehler, Simon A. Gardiner et al.
High-Temperature Atomic Superfluidity in Lattice Boson-Fermion Mixtures
F. Illuminati, A. Albus
Constructive Methods of Invariant Manifolds for Kinetic Problems
A. N. Gorban, I. V. Karlin, A. Yu. Zinovyev