Title 



An efficient finitedifference scheme for computation of electron states in freestanding and coreshell quantum wires
 
Author 



 
Abstract 



The electron states in axially symmetric quantum wires are computed by means of the effectivemass Schrodinger equation, which is written in cylindrical coordinates phi, rho, and z. We show that a direct discretization of the Schrodinger equation by central finite differences leads to a nonsymmetric Hamiltonian matrix. Because diagonalization of such matrices is more complex it is advantageous to transform it in a symmetric form. This can be done by the Liouvillelike transformation proposed by Rizea et al. (2008), which replaces the wave function psi(rho) with the function F(rho) = psi(rho)root rho and transforms the Hamiltonian accordingly. Even though a symmetric Hamiltonian matrix is produced by this procedure, the computed wave functions are found to be inaccurate near the origin, and the accuracy of the energy levels is not very high. In order to improve on this, we devised a finitedifference scheme which discretizes the Schrodinger equation in the first step, and then applies the Liouvillelike transformation to the difference equation. Such a procedure gives a symmetric Hamiltonian matrix, resulting in an accuracy comparable to the one obtained with the finite element method. The superior efficiency of the new finitedifference scheme (FDM) is demonstrated for a few pdependent onedimensional potentials which are usually employed to model the electron states in freestanding and core shell quantum wires. The new scheme is compared with the other FDM schemes for solving the effectivemass Schrodinger equation, and is found to deliver energy levels with much smaller numerical error for all the analyzed potentials. It also gives more accurate results than the scheme of Rizea et al., except for the ground state of an infinite rectangular potential in freestanding quantum wires. Moreover, the PT symmetry is invoked to explain similarities and differences between the considered FDM schemes. (C) 2015 Elsevier B.V. All rights reserved.   
Language 



English
 
Source (journal) 



Computer physics communications.  Amsterdam  
Publication 



Amsterdam : 2015
 
ISSN 



00104655
 
Volume/pages 



197(2015), p. 1726
 
ISI 



000362919500003
 
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