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

Symmetries and (Related) Recursion Operators of Linear Evolution Equations

Received: 28 December 2009; in revised form: 26 January 2010 / Accepted: 29 January 2010 / Published: 5 February 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Download PDF [262 KB, uploaded 5 February 2010]
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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Cicogna G. Symmetries and (Related) Recursion Operators of Linear Evolution Equations. Symmetry. 2010; 2(1):98-111.

Chicago/Turabian Style

Cicogna, Giampaolo. 2010. "Symmetries and (Related) Recursion Operators of Linear Evolution Equations." Symmetry 2, no. 1: 98-111.


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