Divergence-free WKB theory
type: Item
instance of: scholarly article
title: Divergence-free WKB theory
zbMATH Open document ID: 1050.81018
author: Tadanori Hyouguchi
author: Ryohei Seto
author: Masahito Ueda
author: Satoshi Adachi
published in: Annals of Physics
publication date: 2004-08-06T00:00:00Z
review text: Semiclassical theories in quantum dynamics are important, though they are neither classical nor quantum, because they develop new mathematical methods and give useful intuitive insights. The modified WKB theory developed in this paper is based on an approximate reduction of the Schrödinger equation to a cubic algebraic equation in momentum space by including the nonperturbative quantum correction to the usual quadratic approximation. The zeroth-order solution, which is given by a root of the cubic equation includes quantum correction to the bare classical limit \(ip(x;E)\) and is interpreted as a \textit{dressed momentum}. Various ramifications and applications are worked out and discussed.
Mathematics Subject Classification ID: 81Q20
Mathematics Subject Classification ID: 81T16
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 2083545
zbMATH Keywords: semiclassical quantum dynamics
zbMATH Keywords: WKB methods
zbMATH Keywords: divergence
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
full work available at URL: j.aop.2004.01.005
OpenAlex ID: W2093198389
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DOI: 10.1016/J.AOP.2004.01.005
description: scientific article; zbMATH DE number 2083545