TRACE FORMULA FOR GREEN'S FUNCTIONS OF EFFECTIVE MASS SCHRÖDINGER EQUATIONS AND NTH-ORDER DARBOUX TRANSFORMATIONS

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2635-2647 ◽  
Author(s):  
EKATERINA POZDEEVA ◽  
AXEL SCHULZE-HALBERG
Keyword(s):  
Effective Mass ◽  
Trace Formula ◽  
Green's Functions ◽  
Arbitrary Order ◽  
Finite Interval ◽  
Green’S Functions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Mass Case

We derive a trace formula for Green's functions of position-dependent (effective) mass Schrödinger equations that are defined on a real, finite interval and connected by a Darboux transformation of arbitrary order. Our findings generalize former results (J. Phys. A37, 10287 (2004)) on constant mass Schrödinger equations to the effective mass case.

DARBOUX TRANSFORMATIONS FOR N-DIMENSIONAL EFFECTIVE MASS SCHRÖDINGER EQUATIONS WITH HYPERSPHERICAL SYMMETRY

2007 ◽  
Vol 22 (19) ◽  
pp. 3293-3304 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Schrödinger Equation ◽  
Closed Form ◽  
Effective Mass ◽  
Darboux Transformation ◽  
Spherical Symmetry ◽  
Schrodinger Equation ◽  
Arbitrary Order ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations

We construct Darboux transformations of arbitrary order for stationary Schrödinger equations with effective mass that exhibit spherical symmetry in N dimensions (hyperspherical symmetry). The Darboux transformation and the associated transformed Schrödinger equation are obtained in closed form.

REALITY CONDITION FOR DARBOUX TRANSFORMATIONS OF TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4853-4868 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Effective Mass ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Reality Condition ◽  
Set Up

We set up a reality condition for Darboux transformations of time-dependent Schrödinger equations (TDSE) with position-dependent (effective) mass. The reality condition guarantees the potential in the transformed TDSE to be real-valued and hence physical. This paper is a sequel of our former one.36

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 EFFECTIVE MASS SCHRÖDINGER EQUATIONS WITH ENERGY-DEPENDENT POTENTIALS

2008 ◽  
Vol 23 (03n04) ◽  
pp. 537-546 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Effective Mass ◽  
Darboux Transformation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Constant Mass ◽  
Darboux Transformations ◽  
First Order ◽  
Dependent Potential ◽  
Energy Dependent

We construct first-order Darboux transformations for stationary Schrödinger equations with position-dependent (effective) mass and energy-dependent potential. We point out characteristic differences to the corresponding Darboux transformation for constant mass.14

Supersymmetry of time-dependent Schrödinger equations with effective mass

Open Physics ◽  
2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Effective Mass ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations

AbstractWe establish the supersymmetry formalism for time-dependent Schrödinger equations with effective mass and show that the corresponding supersymmetric transformations are equivalent to effective mass Darboux transformations

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