Title 



On improving accuracy of finiteelement solutions of the effectivemass Schrodinger equation for interdiffused quantum wells and quantum wires
 
Author 



 
Abstract 



We use the Galerkin approach and the finiteelement method to numerically solve the effectivemass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation.   
Language 



English
 
Source (journal) 



Communications in theoretical physics.  Wallingford  
Publication 



Wallingford : 2016
 
ISSN 



02536102 [online]
15729494 [print]
 
Volume/pages 



65:1(2016), p. 105113
 
ISI 



000372333900018
 
Full text (publishers version  intranet only) 


  
