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Basis set orthonormality property

  1. Jan 16, 2009 #1
    What does orthonormality of a basis set i.e. {χ_i} stand for? I am reading the Mulliken Population Analysis and there are integrals that are simplified by this property of basis sets and I can't quite catch what is it.
     
  2. jcsd
  3. Jan 16, 2009 #2

    Fredrik

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    Do you know what an inner product (also called scalar product) is? Two vectors u and v are said to be orthogonal if their inner product is zero: <u,v>=0. The quantity

    [tex]\|u\|=\sqrt{\langle u,u\rangle}[/tex]

    is called the norm of u. A basis is said to be orthonormal if all its members have norm 1 and are orthogonal to each other, i.e. if

    [tex]\langle x_i,x_j\rangle=\delta_{ij}[/tex]

    where [itex]\delta_{ij}[/itex] is the Kronecker delta (=1 when i=j, and =0 otherwise).

    Intuitively, you can think of this as meaning that the basis vectors all have length 1 and are perpendicular to each other, but we're really talking about generalizations of those concepts.
     
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