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

QP-PQ, quantum probability and white noise analysis

General Aspects of the Space and Time Transformations for the Coulomb Propagator

Domenico P. L. Castrigiano, F. Staerk

Published Oct 1, 1991• 1 citation
Publisher
DOI
10.1142/9789814360203_0015

Related papers

Space–time transformation for the propagator in de Broglie–Bohm theory

A. Tilbi, Tahar Boudjedaa, M. Merad

Pramana•Sep 28, 2016•3 citations

Feynman propagator and space-time transformation technique

Antonio Boulhosa Nassar

Physica A Statistical Mechanics and its Applications•Feb 1, 1987•12 citations

New aspects of the path integrational treatment of the Coulomb potential

Domenico P. L. Castrigiano, F. Stärk

The well-known treatment of the path integral for the Coulomb potential, by means of the Kustaanheimo–Stiefel transformation and a time transformation, is made more transparent by reducing the problem to the equality of two measures on the space of paths. For this equality two proofs are given: an elementary computational one and a short one recurring to general features of stochastic processes. It is shown that the time transformation is a special case of the well-known time change for a continuous local martingale, by which the process is changed to a Brownian motion and which is determined by its quadratic variation.

Journal of Mathematical Physics•Dec 1, 1989•19 citations

Generalized coherent states for the Coulomb problem in one dimension

S. Nouri

A set of generalized coherent states for the one-dimensional Coulomb problem in coordinate representation is constructed. At first, we obtain a mapping for proper transformation of the one-dimensional Coulomb problem into a nonrotating four-dimensional isotropic harmonic oscillator in the hyperspherical space, and the generalized coherent states for the one-dimensional Coulomb problem is then obtained in exact closed form. This exactly soluble model can provide an adequate means for a quantum coherency description of the Coulomb problem in one dimension, sample for coherent aspects of the exciton model in one-dimension example in high-temperature superconductivity, semiconductors, and polymers. Also, it can be useful for investigating the coherent scattering of the Coulomb particles in one dimension.

Physical Review A•Jun 14, 2002•9 citations

Exact propagators for time-dependent Coulomb, delta and other potentials

V. V. Dodonov, Vladimir I. Man’ko, Dmitri E. Nikonov

Physics Letters A•Feb 1, 1992•65 citations

Time-dependent WKB expansion for the non-relativistic coulomb propagator

S. M. Blinder

Chemical Physics Letters•Feb 1, 1987•3 citations
The well-known treatment of the path integral for the Coulomb potential, by means of the Kustaanheimo–Stiefel transformation and a time transformation, is made more transparent by reducing the problem to the equality of two measures on the space of paths. For this equality two proofs are given: an elementary computational one and a short one recurring to general features of stochastic processes. It is shown that the time transformation is a special case of the well-known time change for a continuous local martingale, by which the process is changed to a Brownian motion and which is determined by its quadratic variation.
A set of generalized coherent states for the one-dimensional Coulomb problem in coordinate representation is constructed. At first, we obtain a mapping for proper transformation of the one-dimensional Coulomb problem into a nonrotating four-dimensional isotropic harmonic oscillator in the hyperspherical space, and the generalized coherent states for the one-dimensional Coulomb problem is then obtained in exact closed form. This exactly soluble model can provide an adequate means for a quantum coherency description of the Coulomb problem in one dimension, sample for coherent aspects of the exciton model in one-dimension example in high-temperature superconductivity, semiconductors, and polymers. Also, it can be useful for investigating the coherent scattering of the Coulomb particles in one dimension.