Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer eBooks

Position Operators for Systems Exhibiting the Special Relativistic Relation Between Momentum and Velocity

Robert F. O’Connell, Eugene Paul Wigner

Published Jan 1, 1997• 0 citations
Publisher
DOI
10.1007/978-3-662-09203-3_31

Related papers

Position operators for systems exhibiting the special relativistic relation between momentum and velocity

Robert F. O’Connell, Eugene Paul Wigner

Physics Letters A•Sep 1, 1978•25 citations

Remarks on the position operator for relativistic elementary systems.

U.E. Schroeder

•Jan 1, 1972•0 citations

Quantum Mechanics and Special Relativity: The Origin of Momentum Operator

Gintautas Kamuntavičius

The free relativistic particle, by definition, has to move in an inertial reference frame with uniform velocity less than the speed of light. The corresponding movement of a material quantum particle describes a wave packet, composed of matter waves—solutions of the Schr?dinger equation. The maximum of packet, corresponding to the largest probability to find the particle, has to move with the same uniform velocity, defined by the initial condition. It has been shown that the traditional definition of the quantum momentum operator i.e. taking it to correspond to the special relativity theory, relativistic momentum, cannot produce precise description of a relativistic matter particle. Different definitions are investigated and one that solves this issue is found. Obtained original expression of relativistic kinetic energy operator creates new possibilities for relativistic quantum systems theory.

Journal of Applied Mathematics and Physics•Jan 1, 2018•0 citations

Why −i∇ is the momentum

Thomas F. Jordan

The operators −i∇, the translation generators, are related to mass and velocity by a simple argument that determines the form of the Hamiltonian, in terms of the translation generators, along with the Galilei generators, for a nonrelativistic particle. For a relativistic particle, a similar discussion is given for the analogous problem of determining the position operators for an irreducible unitary representation of the Poincaré group, at least well enough to identify the velocity operators and thus identify the momentum.

American Journal of Physics•Dec 1, 1975•15 citations

Position Operators of Non-relativistic Quantum Mechanics

Pankaj Sharan

Lecture notes in physics•Jan 1, 2023•0 citations

Velocity Operators and Time-Energy Relations in Relativistic Quantum Mechanics

Mario Bunge

International Journal of Theoretical Physics•Jan 1, 2003•19 citations
The free relativistic particle, by definition, has to move in an inertial reference frame with uniform velocity less than the speed of light. The corresponding movement of a material quantum particle describes a wave packet, composed of matter waves—solutions of the Schr?dinger equation. The maximum of packet, corresponding to the largest probability to find the particle, has to move with the same uniform velocity, defined by the initial condition. It has been shown that the traditional definition of the quantum momentum operator i.e. taking it to correspond to the special relativity theory, relativistic momentum, cannot produce precise description of a relativistic matter particle. Different definitions are investigated and one that solves this issue is found. Obtained original expression of relativistic kinetic energy operator creates new possibilities for relativistic quantum systems theory.
The operators −i∇, the translation generators, are related to mass and velocity by a simple argument that determines the form of the Hamiltonian, in terms of the translation generators, along with the Galilei generators, for a nonrelativistic particle. For a relativistic particle, a similar discussion is given for the analogous problem of determining the position operators for an irreducible unitary representation of the Poincaré group, at least well enough to identify the velocity operators and thus identify the momentum.