The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 3, Issue 18

Question: Wavelets for solide state calculations
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Alexander Schmid (

PostPosted: Mon Dec 02, 2002 1:28 pm    
Subject: Question: Wavelets for solide state calculations
Reply with quote

Question: Wavelets for solide state calculations

Dear Waveletters,

I am considering to compute the wavelet transform of the Schrödinger
equation in a solid. The procedure is the following:

Commonly the pseudopotential method [Ref 1] and the local density
approximation in the density functional formalism [Ref 2] are
carried out for solide state systems. The Schrödinger equation
for an electron with band index $n$ and wave vector ${f k}$ is
written as: $( -{hbar^2over 2m}
abla^2 + V_{eff} )|Psi_{n{f k}}> =
varepsilon_{n{f k}}|Psi_{n{f k}}>$ (1).
For a crystalline solid with a set of reciprocal lattice vectors
${f G}$ and a set of Bloch functions $|{f k}j>$ chosen as the
basis functions to expand the wave function $Psi$:
$|Psi_{n{f k}}> = sum_j c_j^{n{f k}}|{f k}j>$ (2),
where j is a general composite index, Eq. (1) becomes a generalized
matrix equation:
$sum_j <bf k}i|( -{hbar^2over 2m}
abla^2 +
V_{eff}) |{f k}j> c_j^{n{f k}} =
sum_jvarepsilon_{n{f k}}<{f k}i|{f k}j> c_j^{n{f k}}$.
In practice the expansion in Eq. (2) must be truncated at some point,
so that a small number of basis functions gives an accurate
description of the crystal wave function $|Psi_{n{f k}}>$.
Traditional density functional calculations use plane wave basis
sets [Ref 3], where even simple crystal structures (e.g. NaCl, zincblende)
requires a matrix size of $approx 2500$.

Therefore I am looking for a ( wavelet ) basis for $L^2(R^3)$, which

- is independent on the location of the ions in the solid
- is explicitly dependent on the wave vector ${f k}$
- has fast convergence.


[1] G. B. Bachelet, D. R. Hamann, M. Schl"uter,
Phys. Rev. B {f 26}, 4199 (1982)
N. Toullier, J. L. Martins,
Phys. Rev. B {f 43}, 1993 (1991)

[2] P. Hohenberg, W. Kohn,
Phys. Rev. {f 136}, B864 (1964)
W. Kohn, L. J. Sham
Phys. Rev. {f 140}, A1133 (1965)

[3] J. Ihm, A. Zunger, M. l. Cohen
J. Phys. C {f 12}, 4409 (1979)
W. E. Pickett
Comp. Phys. Rep. {f 9}, 115 (1989)

Thank you in advance,

Alexander Schmid
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.025715 seconds : 18 queries executed : GZIP compression disabled