Symmetries and Related Recursion Operators of Linear Evolution EquationsReport as inadecuate




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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





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





Author: Giampaolo Cicogna

Source: http://mdpi.com/



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