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
Completeness relation or closure relation (Read 8992 times)
Gerrit-Jan Linker
YaBB Administrator
*****




Posts: 75
Completeness relation or closure relation
19.01.08 at 12:13:52
 
Completeness relation or closure relation
 
The completeness relation or also called closure relation is often used in the algebra in quantum mechanics:
 
Σi |si><si| = 1 = 1
 
Suppose we have a complete set of orthonormal functions (states) |si>
 
An arbitrary function Ψ can be written as a linear combination: |Ψ>=Σici|si>
 
Multiplying both sides by <sj| gives:
<sj|Ψ> = <sjici|si> <=>
<sj|Ψ> = Σici<sj|si> = Σiciδji = cj <=>  
<sj|Ψ> = cj
 
Thus, |Ψ> = Σici|si> = Σi<si|Ψ>|si> = Σi|si><si|Ψ> <=>
|Ψ> = (Σi|si><si|) |Ψ> thus, Σi|si><si| = 1 = 1
Back to top
 
« Last Edit: 19.01.08 at 12:24:50 by Gerrit-Jan Linker »  

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