Optimally focusing wave packets

Autor:	Wolfgang P. Schleich, Nathan Harshman, L. I. Plimak, R. Mack, P. Kazemi, F Gleisberg, K. Vogel
Rok vydání:	2010
Předmět:	Superposition principle Classical mechanics Chemistry Wave packet Phase space Mathematical analysis Time evolution General Physics and Astronomy Wigner distribution function Position and momentum space Probability density function Physical and Theoretical Chemistry Harmonic oscillator
Zdroj:	Chemical Physics. 375:133-143
ISSN:	0301-0104
Popis:	An appropriately prepared real-valued wave packet moving in one space dimension will focus during a brief period of time even in the absence of any force. We illustrate this phenomenon by considering the time evolution of the elementary superposition of the ground state and the second excited state of a harmonic oscillator. Moreover, we show that a variation of the superposition parameter leads us from a domain of enhanced spreading via a point of suppressed spreading to a region where the wave packets focuses before it spreads again. We determine the points of maximal spreading and optimal focusing. Our analysis of this unusual behavior of a free quantum particle rests on the time dependence of (i) the average separation of the wave packet from the origin, (ii) the probability density in position space, and (iii) the Wigner phase space distribution. We conclude our search for optimally focusing wave packets by solving the corresponding variational problem with respect to a family of measures expressing the width of the wave packet.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7aa15e7089a889ed6104e0210c87c6c5 https://doi.org/10.1016/j.chemphys.2010.07.002 Zobrazit plný text záznamu Full Text from ScienceDirect