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Abstract
We propose a numerical algorithm based on a discrete variable representation and shifted inverse iterations and apply it to for the analysis of the bound states of edge dislocation modelled by a quantum dipole in a plane. The good agreement with results of recent papers of Amore et al [J. Phys. B 45, 235004 (2012)] was obtained. The error estimates of the previous results of low-lying states energies of other authors were not known due to limitations of the variational approaches and this paper fills this gap presenting calculated low-lying bound states energies by non-variational technique. The probability densities of low-lying states were calculated.
Highlights
The aim of this paper is study the low-lying bound states of the straight edge dislocation in solids
Due to the nonseparability of the potential (1) the quantitative analysis is difficult because traditional analytical techniques are no longer applicable and effective numerical methods are required for solving of the full Shrödinger equation. We propose such a numerical algorithm and numerically solve the corresponding two-dimensional (2D) Schrödinger equation [1]:
In the paper [1] it was noted, that the RDSM methods are preferable for low-lying states than variational studies, but the best ground state energy (GSE) value (-0.139 arb.u.) was calculated by RDSM only with 2% accuracy
Summary
The aim of this paper is study the low-lying bound states of the straight edge dislocation in solids. In the paper [1] it was noted, that the RDSM methods are preferable for low-lying states than variational studies, but the best GSE value (-0.139 arb.u.) was calculated by RDSM only with 2% accuracy. Amore et al [12] showed, that variational technique for Slater-type orbitals are converged faster and seems to be more accurate for the GSE value, than the Coulomb basis set. [12], that, possibly, bad convergence of variational studies for low-lying states comes from limited accuracy of the method due to not complete basis of the basis function set. Handy et al [13] proved this statement, expanding the wave function over a complete basis with the help of an orthogonal polynomial projection quantization analysis, which substantially decreased the needed for convergence variational parameters number
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