We reformulate the theory of ordinary differential equations of arbitrary order with nonconstant coefficients, using the formalism of non-Hermitian operators. In particular, exploiting the technique of dissipative quantum mechanics, we show that the solution of the equations can be written in terms of a nonunitary evolution operator. Furthermore, we point out that the solution of the adjoint equations can be derived from an associated biunitary operator. We show that a number of invariants, not previously discussed, exhists. Finally, we prove that the method allows the search for approximate solutions that can be used in many physical problems.

Biunitary transformations and ordinary differential equations - I / 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. - 106B:(1991), pp. 1357-1374. [10.1007/BF02728366]

Biunitary transformations and ordinary differential equations - I

LORETO, Vittorio;
1991

Abstract

We reformulate the theory of ordinary differential equations of arbitrary order with nonconstant coefficients, using the formalism of non-Hermitian operators. In particular, exploiting the technique of dissipative quantum mechanics, we show that the solution of the equations can be written in terms of a nonunitary evolution operator. Furthermore, we point out that the solution of the adjoint equations can be derived from an associated biunitary operator. We show that a number of invariants, not previously discussed, exhists. Finally, we prove that the method allows the search for approximate solutions that can be used in many physical problems.
1991
01 Pubblicazione su rivista::01a Articolo in rivista
Biunitary transformations and ordinary differential equations - I / 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. - 106B:(1991), pp. 1357-1374. [10.1007/BF02728366]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/449647
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