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Symmetry 2010, 2(1), 98-111; doi:10.3390/sym2010098

Symmetries and (Related) Recursion Operators of Linear Evolution Equations

Dipartimento di Fisica “E. Fermi” dell’Universit`a di Pisa and INFN, sez. di Pisa, Largo B. Pontecorvo 3, Ed. B-C, I-56127–Pisa, Italy
Received: 28 December 2009 / Revised: 26 January 2010 / Accepted: 29 January 2010 / Published: 5 February 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Abstract

Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant) notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.
Keywords: recursion operators; step up/down operators; Lie point symmetries; Schrödinger equation; Fokker–Planck equation recursion operators; step up/down operators; Lie point symmetries; Schrödinger equation; Fokker–Planck equation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Cicogna, G. Symmetries and (Related) Recursion Operators of Linear Evolution Equations. Symmetry 2010, 2, 98-111.

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