scholarly journals Infinite families of position-dependent mass Schrödinger equations with known ground and first excited states

2018 ◽  
Vol 399 ◽  
pp. 270-288 ◽  
Author(s):  
C. Quesne
Keyword(s):  
Excited States ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Dependent Mass ◽  
Position Dependent Mass

Position-dependent mass Schrödinger equations allowing harmonic oscillator (HO) eigenvalues

2008 ◽  
Vol 108 (15) ◽  
pp. 2906-2913 ◽  
Author(s):  
J. J. Peña ◽  
G. Ovando ◽  
J. Morales ◽  
J. GarcÍa-Ravelo ◽  
C. Pacheco-García
Keyword(s):  
Harmonic Oscillator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Dependent Mass ◽  
Position Dependent Mass

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.

Exactly solvable Schrödinger equations with a position-dependent mass: Null potential

2007 ◽  
Vol 107 (15) ◽  
pp. 3039-3045 ◽  
Author(s):  
J. J. Peña ◽  
G. Ovando ◽  
J. Morales ◽  
J. García-Ravelo ◽  
C. Pacheco-García
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exactly Solvable ◽  
Dependent Mass ◽  
Position Dependent Mass

AN IMPLICIT SPECTRAL FORMULA FOR GENERALIZED LINEAR SCHRÖDINGER EQUATIONS

2009 ◽  
Vol 18 (09) ◽  
pp. 1831-1844 ◽  
Author(s):  
AXEL SCHULZE-HALBERG ◽  
JESÚS GARCÍA-RAVELO ◽  
JOSÉ JUAN PEÑA GIL
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Complete Spectrum ◽  
Quantization Rule ◽  
Special Cases ◽  
Dependent Mass ◽  
Spectral Formula ◽  
Position Dependent Mass

We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schrödinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schrödinger equation or the Schrödinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form.

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.

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