Summary
In this paper we consider the evolution equations which are associated to the Schrödinger matrix problem for triangular matrices, a very simple subclass of the non-Hermitian matrices. These evolution equations, though linear in the simple case considered in the present paper, are not all solvable by means of standard techniques, thus making it worthwhile exploiting the applicability of the inverse spectral transform to obtain particular solutions. The 2 × 2 case is investigated thoroughly.
Riassunto
In questo articolo si studiano le equazioni di evoluzione associate all’equazione matriciale di Schrödinger nel easo di matrici triangolari, una classe assai semplice di matrici non hermitiane. Tali equazioni di evoluzione, anche se lineari nel caso qui considerato, non sono tutte risolubili con tecniche standard: di qui l’interesse di utilizzare la tecnica della trasformata spettrale inversa per trovare delle soluzioni particolari. Si esamina in dettaglio il caso di matrici triangolari 2 × 2.
Реэюме
В зтой работе мы рассматриваем уравнения зволюции, свяэанные с проблемой Щредингера для треугольных матриц, очень простого подкласса не-эрмитовых матриц. Эти уравнения зволюции, хотя они являются линейными в рассмотренном в работе случае, не могут быть рещены с помощью стандартной техники. В свяэи с зтим испольэуется обратное спектральное преобраэование для получения частных рещений. Исследуется случай 2 × 2.
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In this case the Bergmann strip (7) extends to the whole complexk-plane.
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Bruschi, M., Levi, D. & Ragnisco, O. Evolution equations associated to the triangular-matrix Schrödinger problem solvable by the inverse spectral transform. Nuov Cim A 45, 225–237 (1978). https://doi.org/10.1007/BF02724665
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DOI: https://doi.org/10.1007/BF02724665