English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

The electron states in axially symmetric quantum wires are computed by meansof the effective-mass Schroedinger equation, which is written in cylindricalcoordinates phi, rho, and z. We show that a direct discretization of theSchroedinger equation by central finite differences leads to a non-symmetricHamiltonian matrix. Because diagonalization of such matrices is more complex itis advantageous to transform it in a symmetric form. This can be done by theLiouville-like transformation proposed by Rizea et al. (Comp. Phys. Comm. 179(2008) 466-478), which replaces the wave function psi(rho) with the functionF(rho)=psi(rho)sqrt(rho) and transforms the Hamiltonian accordingly. Eventhough a symmetric Hamiltonian matrix is produced by this procedure, thecomputed wave functions are found to be inaccurate near the origin, and theaccuracy of the energy levels is not very high. In order to improve on this, wedevised a finite-difference scheme which discretizes the Schroedinger equationin the first step, and then applies the Liouville-like transformation to thedifference equation. Such a procedure gives a symmetric Hamiltonian matrix,resulting in an accuracy comparable to the one obtained with the finite elementmethod. The superior efficiency of the new finite-difference (FDM) scheme isdemonstrated for a few rho-dependent one-dimensional potentials which areusually employed to model the electron states in free-standing and core-shellquantum wires. The new scheme is compared with the other FDM schemes forsolving the effective-mass Schroedinger equation, and is found to deliverenergy levels with much smaller numerical error for all the analyzedpotentials. Moreover, the PT symmetry is invoked to explain similarities anddifferences between the considered FDM schemes.

An efficient finite-difference scheme for computation of electron states in free-standing and core-shell quantum wires