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

Publisher:
Wiley-VCH Verlag GmbH & Co. KGaA
Publication Type:
Chapter
Citation:
Non-diffracting Waves, 2014, pp. 189 - 209
Issue Date:
2014
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© 2014 Wiley-VCH Verlag GmbH & Co. KGaA. 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. Controlled Vocabulary Terms: Schrodinger equation
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