We consider rectilinear free-space propagation of electromagnetic wavepackets using electromagnetic field theory, scalar wavepacket propagation, and quantum-mechanical formalism. We demonstrate that spatially localized wavepackets are inherently characterized by a subluminal group velocity and a superluminal phase velocity, whose product equals $c^2$ . These velocities are also known as the 'energy' and 'momentum' velocities, introduced by K. Milton and J. Schwinger. We illustrate general conclusions by explicit calculations for Gaussian and higher-order beams and wavepackets, and also highlight subtleties of the quantum-mechanical description based on the 'photon wavefunction'.We consider rectilinear free-space propagation of electromagnetic wavepackets using electromagnetic field theory, scalar wavepacket propagation, and quantum-mechanical formalism. We demonstrate that spatially localized wavepackets are inherently characterized by a subluminal group velocity and a superluminal phase velocity, whose product equals $c^2$. These velocities are also known as the 'energy' and 'momentum' velocities, introduced by K. Milton and J. Schwinger. We illustrate general conclusions by explicit calculations for Gaussian and higher-order beams and wavepackets, and also highlight subtleties of the quantum-mechanical description based on the 'photon wavefunction'.

quant-pharXiv:2602.17576Feb 20, 2026

Adiabatic Wavepacket Propagation

M. Jääskeläinen, Stig Stenholm

Springer eBooksJan 1, 20030 citations

Wavepacket mode analysis in quantum mechanics

G.J. Papadopoulos

Physics Letters ASep 1, 19855 citations

Free temporal evolution of a superbandwidth wave packet: The quantum tale of the hare and the tortoise

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.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.

arXiv:2501.06001Jan 10, 20250 citations

Quantum wave packet propagation

J. Broeckhove, Luc Lathouwers, Piet Van Leuven

Jan 1, 19870 citations

c^2

. These velocities are also known as the 'energy' and 'momentum' velocities, introduced by K. Milton and J. Schwinger. We illustrate general conclusions by explicit calculations for Gaussian and higher-order beams and wavepackets, and also highlight subtleties of the quantum-mechanical description based on the 'photon wavefunction'.