Linker IT Software
menubar-top-links menubar-top-rechts
Home Help Search Login
Welcome, Guest. Please Login.
SQL*XL: Database to Excel bridge litLIB: Excel power functions pack ExcelLock: Locking and securing your valuable Excel spreadsheets encOffice: Protect your Excel file easy and safe encOffice: Protect your Excel file easy and safe
Pages: 1
Total Electron Density (Read 2666 times)
Gerrit-Jan Linker
YaBB Administrator

Posts: 75
Total Electron Density
27.02.08 at 23:35:31
Total Electron Density
Probability density:
In the Born interpretation, the probability density is  
The probability density is the probability of finding electron 1 in a volume element dr around r1, electron2 in a volume element dr around r2, ...
Assumptions: ψ is a physically permissible, normalised wavefunction.
Integration over all space yields the number of electrons  
N=∫dr1dr2dr3...drN ψ(r1,r2,r3,...,rN)ψ(r1,r2,r3,...,rN)
The chance of locating particle one in a volume element dr around r1, irrespective the location of the other variables is:
dx1∫dr2dr3...drN ψ(r1,r2,r3,...,rN)ψ(r1,r2,r3,...,rN)
The chance to locate any particle from a collection of N independent particles is:
ρ(x1)dx1=Ndx1∫dr2dr3...drN ψ(r1,r2,r3,...,rN)ψ(r1,r2,r3,...,rN)
Integration over all spin variables (collectively s) gives the charge density in a pont in space:
The density matrices are a representation, in the basis set of the electron density at a point in space.  
The total density can be subdivided into the probability of finding a spin-up (alpha) electron plus the probability of finding a spin-down (beta) electron.
Back to top
« Last Edit: 13.11.13 at 12:06:22 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
Email WWW Gerrit-Jan Linker   IP Logged
Pages: 1