Linker IT Software
Google
Web www.oraxcel.com
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
Pauli Exclusion Principle (Read 5289 times)
Gerrit-Jan Linker
YaBB Administrator
*****




Posts: 75
Pauli Exclusion Principle
20.02.08 at 12:27:26
 
Pauli Exclusion Principle
 
Because of the quantum mechanical Uncertainty Principle, quantum mechanics methods treat electrons as indistinguishable particles. This leads to the Pauli Exclusion Principle, which states that the many-electron wave function—which depends on the coordinates of all the electrons—must change sign whenever two electrons interchange positions. That is, the wave function must be antisymmetric with respect to pair-wise permutations of the electron coordinates.  
 
The Exclusion Principle is quantum mechanical in nature, and outside the realm of everyday, "classical" experience. Think of it as the inherent tendency of electrons to stay away from one another; to be mutually excluded. Exclusion is due to the antisymmetry of the wave function and not to electrostatic coulomb repulsion between two electrons. Exclusion exists even in the absence of electrostatic repulsions.  
 
Quotation from j.chem.edu Gillespie (2004):
Quote:

...electrons with the same spin have a zero probability of being found at the same location, and an increasing probability  of  being  found  at  an  increasing  distance  apart.

It can, perhaps, be useful to think of opposite spin α and β (or spin-up and spin-down) electrons as existing in two independent “worlds”  (two  independent,  but  overlapping,  sets  of  three dimensions) in which, if we ignore their mutual electrostatic repulsion,  the  α  electrons  do  not  “see”  the  β  electrons  in the  other  “world”  and  so  they  have  no  influence  on  each other’s behavior, whereas electrons of the same spin in the same “world” have to share the space available to them andthus, keep as far apart as possible.

 
Gillespie, "Chemical Bonding and Molecular Geometry: From Lewis to Electron Densities, 2001, p74
Quote:
Electrons   with   the   same   spin   have   a   zero   probability   of   being   found simultaneously at the same point in space, a low probability of being found close together, and are most probably to be found as far apart as possible.  

 
See also:
Pauli Blocking
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1342027318/0#0
Back to top
 
« Last Edit: 11.07.12 at 19:22:28 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
Email WWW Gerrit-Jan Linker   IP Logged
Gerrit-Jan Linker
YaBB Administrator
*****




Posts: 75
Re: Pauli Exclusion Principle
Reply #1 - 28.07.08 at 16:42:27
 
Quote:
...Because electrons are indistinguishable, the order in which their variables appear in the wave function should be immaterial to the value of the observables of the system. For the probability density of a two particle system, given by:

ρ(x1,x2) = Ψ*(x1,x2)Ψ(x1,x2) = Φ*(x2,x1)Φ(x2,x1)

this condition implies either Φ(x2,x1) = Ψ(x1,x2) or Φ(x2,x1) = -Ψ(x1,x2). It has een found that for electrons the wave function should be antisymmetric with respect to particle interchange, i.e. the second relation holds. This requirement on the wave function is called the Pauli principle...

 
Source: thesis Alex de Vries
Back to top
 
« Last Edit: 28.07.08 at 16:46:29 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
Email WWW Gerrit-Jan Linker   IP Logged
Gerrit-Jan Linker
YaBB Administrator
*****




Posts: 75
Wave function anti-symmetry
Reply #2 - 27.08.09 at 13:14:04
 
Wave function anti-symmetry
 
The requirement that a wave function should be anti-symmetric due to the Pauli principle is fulfilled when we use an anti-symmetrized product of orbitals. Such a product can be writen as a Slater determinant.
Back to top
 
 

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