Wavepacket mode analysis in quantum mechanics

Donald Jack Kouri, Youhong Huang, David K. Hoffman

John R. Merrill

Enrique G. Neyra, Marcelo F. Ciappina, Lorena Rebón

Can the interplay between quantum mechanics and classical optics offer new perspectives on wavepacket dynamics? Building on this connection, we show that local momenta with both super-oscillatory and suboscillatory characteristics can arise during the free propagation of a quantum particle. This behavior is mathematically analogous to the propagation of a superbandwidth laser pulse in a dispersive medium, where the instantaneous frequencies of the electric field exhibit similar sub- and super-oscillatory features. This analogy is rooted in the equivalence between the wave description of light in classical optics and the formalism of quantum mechanics. In addition, we explore the phenomenon of wavepacket localization during free propagation within a bounded region. This localization is directly linked to the distribution of local momenta within the confined wavepacket region. To complement our quantum mechanical analysis, we also perform a classical analysis to provide further insights into this phenomenon. Our findings reveal that both the emergence of local momenta with sub- and super-oscillatory features and the wavepacket localization occur within a distinct timescale, which we define as the interference time.

Mark Sheard Child

Abstract The discussion in previous chapters has centred on the use of trajectorybased information to add quantum corrections to the classical picture, in a mainly time-independent picture. This chapter takes an explicitly timedependent standpoint by examining the relevance of various types of wavepacket to classical mechanics and vice versa; Littlejohn (1986) gives a much fuller mathematical account. The intuitive connection is obvious, in the sense that a unit normalized wavepacket corresponds most nearly to a single quantum mechanical particle, but the associated uncertainty relations imply a closer connection with a classical ensemble. Analysis of this connection is one of the main concerns of the first half of the chapter.

Enrique J. Galvez, Jake M. Freedman, Anupama Motee

Exploiting similarities between the Schrödinger and Helmholtz equations we prepare optical beams that simulate quantum solutions of the simple mechanical pendulum. We did laboratory investigations of optical patterns that correlated with the probabilities in the quantum pendulum. Coherent superpositions of modes simulated quantum wavepackets in the linear-harmonic-oscillator and nonlinear-Mathieu regimes.

Róbert E. Wyatt