Exact analytic solution of position-dependent mass Schrödinger equation

2017 ◽  
Vol 92 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Hangshadhar Rajbongshi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Analytic Solution ◽  
Exact Analytic Solution ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals Position-Dependent Mass Schrödinger Equation for the Morse Potential

2017 ◽  
Vol 792 ◽  
pp. 012037 ◽  
Author(s):  
G Ovando ◽  
J J Peña ◽  
J Morales ◽  
J López-Bonilla
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Morse Potential ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals On the position-dependent mass Schrödinger equation for Mie-type potentials

2021 ◽  
Vol 2090 (1) ◽  
pp. 012165
Author(s):  
G Ovando ◽  
J J Peña ◽  
J Morales ◽  
J López-Bonilla
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Operator ◽  
Constant Mass ◽  
Point Canonical Transformation ◽  
Mass Distributions ◽  
Exactly Solvable ◽  
Reference Problem ◽  
Dependent Mass ◽  
Position Dependent Mass

Abstract The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

scholarly journals EXACT SOLUTION OF THE SCHRÖDINGER EQUATION FOR THE MODIFIED KRATZER'S MOLECULAR POTENTIAL WITH POSITION-DEPENDENT MASS

2008 ◽  
Vol 17 (07) ◽  
pp. 1327-1334 ◽  
Author(s):  
RAMAZÀN SEVER ◽  
CEVDET TEZCAN
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Dependent Mass ◽  
Morse Potentials ◽  
Position Dependent Mass

Exact solutions of Schrödinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

Scattering states of the Schrödinger equation with a position-dependent-mass and a non-central potential

2016 ◽  
Vol 69 (11) ◽  
pp. 1619-1624 ◽  
Author(s):  
M. Chabab ◽  
A. El Batoul ◽  
M. Oulne ◽  
H. Hassanabadi ◽  
S. Zare
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Central Potential ◽  
Scattering States ◽  
Dependent Mass ◽  
Position Dependent Mass
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