In two previous papers, the authors have introduced the concept of binormal differential equations. It has been shown that invariants of the Courant-Snyder type are associated to the scalar products of the column vector associated to an ordinary differential equation and to its binormal. In this paper, we show the equivalence of the above invariant and the Lewis form. We also introduce a density matrix for a second-order differential equation and clarify the geometrical meaning of the Twiss parameters. The importance of the above results in the analysis of quantum problems such as, e.g., the evolution of squeezed states is finally stressed.
Biunitary transformations and ordinary differential equations - III / G., Dattoli; Loreto, Vittorio; C., Mari; M., Richetta; A., Torre. - In: LA RIVISTA DEL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. - ISSN 0393-697X. - STAMPA. - 106 B:12(1991), pp. 1391-1399. [10.1007/BF02728368]
Biunitary transformations and ordinary differential equations - III
LORETO, Vittorio;
1991
Abstract
In two previous papers, the authors have introduced the concept of binormal differential equations. It has been shown that invariants of the Courant-Snyder type are associated to the scalar products of the column vector associated to an ordinary differential equation and to its binormal. In this paper, we show the equivalence of the above invariant and the Lewis form. We also introduce a density matrix for a second-order differential equation and clarify the geometrical meaning of the Twiss parameters. The importance of the above results in the analysis of quantum problems such as, e.g., the evolution of squeezed states is finally stressed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.