Symmetries and (Related) Recursion Operators of Linear Evolution Equations

Symmetry

关键词: recursion operators;    step up/down operators;    Lie point symmetries;    Schrödinger equation;    Fokker–Planck equation;   

DOI  :  10.3390/sym2010098

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.