# Symmetries and (Related) Recursion Operators of Linear Evolution Equations

## Abstract

**:**

## 1. Introduction

## 2. The recursion and the step up/down operators

**Proposition**

**1**

**Proposition**

**2**

**Proposition**

**3**

## 3. The Schrödinger equation

**Theorem**

**4**

#### 3.1. The Schrödinger equation for the harmonic oscillator and for the free particle

#### 3.2. The Schrödinger equation with $V\left(x\right)\propto {x}^{2}+\delta /{x}^{2}$

#### 3.3. The effect of a centrifugal potential in $q>1$ dimensions

## 4. The Fokker–Planck equation

#### 4.1. The presence of four linearly independent nontrivial symmetries

#### 4.2. The presence of two independent nontrivial symmetries

## 5. Concluding remarks

## Acknowledgements

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**MDPI and ACS Style**

Cicogna, G.
Symmetries and (Related) Recursion Operators of Linear Evolution Equations. *Symmetry* **2010**, *2*, 98-111.
https://doi.org/10.3390/sym2010098

**AMA Style**

Cicogna G.
Symmetries and (Related) Recursion Operators of Linear Evolution Equations. *Symmetry*. 2010; 2(1):98-111.
https://doi.org/10.3390/sym2010098

**Chicago/Turabian Style**

Cicogna, Giampaolo.
2010. "Symmetries and (Related) Recursion Operators of Linear Evolution Equations" *Symmetry* 2, no. 1: 98-111.
https://doi.org/10.3390/sym2010098