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European Journal of Physics

Distance between quantum states and the motion of wave packets

R. v. Baltz

Published Jul 1, 1990• 17 citations
Publisher

Abstract

A definition of the distance between two quantum states is given which is independent of the (global) phase of the wavefunction. For example, wave packets for the harmonic oscillator and a particle in a box potential are investigated.
DOI
10.1088/0143-0807/11/4/004

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We revisit multi-slit diffraction with a scaling of space and time to exploit an equivalence of wave packets describing quantum free and harmonic oscillator (HO) motion. We introduce a co-moving frame of space and time coordinates to define an effective, time-independent, HO potential that confines and directs initially displaced wave packets along the classical phase space of the oscillator. NNN-slit diffraction in the lab frame from the slits to a distant detector and the familiar spreading of the propagating wave front is then described as the propagation of HO wave packets over just a quarter cycle of the oscillator and confined to the HO potential well. This connection with the co-moving frame suggests a simplified time of flight experiment wherein the arrival time distribution of diffracted particles hitting a \emph{single point detector} in the lab frame images in the co-moving frame as the \emph{full} diffraction pattern from grating to detector.
ABSTRACT We revisit multi‐slit diffraction with a scaling of space and time to exploit an equivalence of wave packets describing quantum free and harmonic oscillator (HO) motion. We introduce a co‐moving frame of space and time coordinates to define an effective, time‐independent, HO potential that confines and directs initially displaced wave packets along the classical phase space of the oscillator. ‐slit diffraction in the lab frame from the slits to a distant detector and the familiar spreading of the propagating wave front is then described as the propagation of HO wave packets over just a quarter cycle of the oscillator and confined to the HO potential well. We show that diffraction features are preserved in the co‐moving frame and well characterized in both the near and far fields by the classical trajectories of the HO phase space.