Linearly traveling and accelerating localized wave solutions to the schrödinger and schrödinger-like equations

Ioannis M. Besieris; Amr M. Shaarawi; Richard W. Ziolkowski

doi:10.1002/9783527671519.ch7

Linearly traveling and accelerating localized wave solutions to the schrödinger and schrödinger-like equations

Ioannis M. Besieris, Amr M. Shaarawi, Richard W. Ziolkowski

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

Summary: This chapter demonstrates that one can derive nondispersive localized wave packet solutions to the Schrödinger equation. Two ansätze are formulated that allow a large class of infinite- and finite-energy, nonsingular, localized, linearly traveling wave solutions to the linear 3D Schrödinger equation to be obtained. The chapter provides an account of a broad class of finite-energy accelerating localized wave solutions to the 3D Schrödinger equation based on a generalization of previous work on one-dimensional (1D) infinite-energy nonspreading wave packets. It contains derivations of linearly traveling and accelerating localized wave solutions to 3D Schrödinger-like equations arising in propagation through transparent anomalous and normal dispersive media, with emphasis on analytical finite-energy wavepackets.

Original language	English (US)
Title of host publication	Non-diffracting Waves
Publisher	Wiley-VCH Verlag
Pages	189-209
Number of pages	21
ISBN (Electronic)	9783527671519
ISBN (Print)	9783527411955
DOIs	https://doi.org/10.1002/9783527671519.ch7
State	Published - Oct 4 2013
Externally published	Yes

Keywords

Localized wave packet solutions
Schrödinger-like equations

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1002/9783527671519.ch7

Cite this

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title = "Linearly traveling and accelerating localized wave solutions to the schr{\"o}dinger and schr{\"o}dinger-like equations",

abstract = "Summary: This chapter demonstrates that one can derive nondispersive localized wave packet solutions to the Schr{\"o}dinger equation. Two ans{\"a}tze are formulated that allow a large class of infinite- and finite-energy, nonsingular, localized, linearly traveling wave solutions to the linear 3D Schr{\"o}dinger equation to be obtained. The chapter provides an account of a broad class of finite-energy accelerating localized wave solutions to the 3D Schr{\"o}dinger equation based on a generalization of previous work on one-dimensional (1D) infinite-energy nonspreading wave packets. It contains derivations of linearly traveling and accelerating localized wave solutions to 3D Schr{\"o}dinger-like equations arising in propagation through transparent anomalous and normal dispersive media, with emphasis on analytical finite-energy wavepackets.",

keywords = "Localized wave packet solutions, Schr{\"o}dinger-like equations",

author = "Besieris, {Ioannis M.} and Shaarawi, {Amr M.} and Ziolkowski, {Richard W.}",

note = "Publisher Copyright: {\textcopyright} 2014 Wiley-VCH Verlag GmbH & Co. KGaA.",

year = "2013",

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doi = "10.1002/9783527671519.ch7",

language = "English (US)",

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T1 - Linearly traveling and accelerating localized wave solutions to the schrödinger and schrödinger-like equations

AU - Besieris, Ioannis M.

AU - Shaarawi, Amr M.

AU - Ziolkowski, Richard W.

PY - 2013/10/4

Y1 - 2013/10/4

N2 - Summary: This chapter demonstrates that one can derive nondispersive localized wave packet solutions to the Schrödinger equation. Two ansätze are formulated that allow a large class of infinite- and finite-energy, nonsingular, localized, linearly traveling wave solutions to the linear 3D Schrödinger equation to be obtained. The chapter provides an account of a broad class of finite-energy accelerating localized wave solutions to the 3D Schrödinger equation based on a generalization of previous work on one-dimensional (1D) infinite-energy nonspreading wave packets. It contains derivations of linearly traveling and accelerating localized wave solutions to 3D Schrödinger-like equations arising in propagation through transparent anomalous and normal dispersive media, with emphasis on analytical finite-energy wavepackets.

AB - Summary: This chapter demonstrates that one can derive nondispersive localized wave packet solutions to the Schrödinger equation. Two ansätze are formulated that allow a large class of infinite- and finite-energy, nonsingular, localized, linearly traveling wave solutions to the linear 3D Schrödinger equation to be obtained. The chapter provides an account of a broad class of finite-energy accelerating localized wave solutions to the 3D Schrödinger equation based on a generalization of previous work on one-dimensional (1D) infinite-energy nonspreading wave packets. It contains derivations of linearly traveling and accelerating localized wave solutions to 3D Schrödinger-like equations arising in propagation through transparent anomalous and normal dispersive media, with emphasis on analytical finite-energy wavepackets.

KW - Localized wave packet solutions

KW - Schrödinger-like equations

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DO - 10.1002/9783527671519.ch7

M3 - Chapter

AN - SCOPUS:85017419296

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SP - 189

EP - 209

BT - Non-diffracting Waves

PB - Wiley-VCH Verlag

ER -

Linearly traveling and accelerating localized wave solutions to the schrödinger and schrödinger-like equations

Abstract

Keywords

ASJC Scopus subject areas

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