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Orthonormal basis sets - Kronecker delta function (Read 5097 times)
Gerrit-Jan Linker
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Orthonormal basis sets - Kronecker delta function
14.01.08 at 21:14:29
 
Orthonormal basis sets - Kronecker delta function
 
The Kronecker delta function dij = 0 if not i=j, and 1 if i=j.
 
A vector set V is said to be orthonormal if the scalar product of any two vectors is equal to the Kronecker delta function.
 
if {|i>}N is the basis set, for any vector |i> of that basis set there is a vector |j> that is also member of the basis set for which <i|j> = dij
 
It is always possible to choose any basis set and orthogonalize and normalize it a posteriori
 
The product of any two vectors a.b = a.b.cos(fi) where a and b are the magnitudes (lengths) of vectors a and b and where fi is the angle between the two vectors.  
If the vectors are orthogonal the angle is 90 degrees and cos(fi) = 0
 
See also:
Scalar product of vectors
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1200341195
Orthonormal basis
http://en.wikipedia.org/wiki/Orthonormal_basis
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« Last Edit: 15.01.08 at 22:47:08 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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