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Bi-unitary transformation and ordinary differential equations: Part 3

Technical Report:

Abstract

In two previous papers, the authors introduced the concept of binormal differential equations. It was shown that invariants of the Courant-Snyder type are associated with the scalar products of the column vectors associated to an ordinary differential equation and to its binormal. This paper shows the equivalence of the above invariant and the Lewis form. It also introduces a density matrix for a second-order differential equation and clarifies the geometrical meaning of Twiss parameters. Within the framework of accelerator physics, the importance of the above results in the analysis of quantum problems such as the evolution of squeezed states is stressed.
Publication Date:
Sep 01, 1991
Product Type:
Technical Report
Report Number:
ENEA-RT-INN-90-32; RT/INN-90-32
Reference Number:
SCA: 430200; 661100; PA: ITAN-91:002089; SN: 92000621827
Resource Relation:
Other Information: PBD: Sep 1991
Subject:
43 PARTICLE ACCELERATORS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BEAM DYNAMICS; DIFFERENTIAL EQUATIONS; QUANTUM MECHANICS; QUANTUM ELECTRONICS; 430200; 661100; BEAM DYNAMICS, FIELD CALCULATIONS, AND ION OPTICS; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10107666
Research Organizations:
ENEA, Frascati (Italy). Dipt. Sviluppo Tecnologie di Punta
Country of Origin:
Italy
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 1120-558X; Other: ON: DE92744018; TRN: 91:002089
Availability:
OSTI; NTIS (US Sales Only)
Submitting Site:
ITAN
Size:
20 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Dattoli, G, Loreto, V, Mari, C, Richetta, M, and Torre, A. Bi-unitary transformation and ordinary differential equations: Part 3. Italy: N. p., 1991. Web.
Dattoli, G, Loreto, V, Mari, C, Richetta, M, & Torre, A. Bi-unitary transformation and ordinary differential equations: Part 3. Italy.
Dattoli, G, Loreto, V, Mari, C, Richetta, M, and Torre, A. 1991. "Bi-unitary transformation and ordinary differential equations: Part 3." Italy.
@misc{etde_10107666,
title = {Bi-unitary transformation and ordinary differential equations: Part 3}
author = {Dattoli, G, Loreto, V, Mari, C, Richetta, M, and Torre, A}
abstractNote = {In two previous papers, the authors introduced the concept of binormal differential equations. It was shown that invariants of the Courant-Snyder type are associated with the scalar products of the column vectors associated to an ordinary differential equation and to its binormal. This paper shows the equivalence of the above invariant and the Lewis form. It also introduces a density matrix for a second-order differential equation and clarifies the geometrical meaning of Twiss parameters. Within the framework of accelerator physics, the importance of the above results in the analysis of quantum problems such as the evolution of squeezed states is stressed.}
place = {Italy}
year = {1991}
month = {Sep}
}