Arbitrary-order Darboux transformations for two-dimensional Dirac equations with position-dependent mass

2020 ◽  
Vol 135 (3) ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Arbitrary Order ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Equations ◽  
Dependent Mass ◽  
Position Dependent Mass

Generalized linear Schrödinger equations and their Darboux transformations

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Vector Potential ◽  
Arbitrary Order ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Weighted Energy ◽  
Dependent Mass ◽  
Position Dependent Mass

AbstractWe construct explicit Darboux transformations of arbitrary order for a class of generalized, linear Schrödinger equations. Our construction contains the well-known Darboux transformations for Schrödinger equations with position-dependent mass, Schrödinger equations coupled to a vector potential and Schrödinger equations for weighted energy.

DARBOUX TRANSFORMATIONS FOR TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS

2006 ◽  
Vol 21 (06) ◽  
pp. 1359-1377 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Wave Function ◽  
Darboux Transformation ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Explicit Formulas ◽  
The Difference ◽  
Dependent Mass ◽  
Position Dependent Mass

The formalism of Darboux transformations is established for time-dependent Schrödinger equations with an effective (position-dependent) mass. Explicit formulas are obtained for the transformed wave function and the difference between the original and the transformed potential. It is shown that for a noneffective mass our Darboux transformation reduces correctly to the well-known Darboux transformation.

Sign in / Sign up

Export Citation Format

Share Document