Basis set orthonormality property

  • Thread starter filippo
  • Start date
  • #1
12
0
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.
 

Answers and Replies

  • #2
Fredrik
Staff Emeritus
Science Advisor
Gold Member
10,851
413
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.
 

Related Threads on Basis set orthonormality property

Replies
1
Views
243
  • Last Post
Replies
3
Views
913
Replies
2
Views
582
  • Last Post
Replies
15
Views
6K
Replies
21
Views
4K
Replies
5
Views
3K
  • Last Post
Replies
3
Views
18K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
2
Views
4K
Replies
11
Views
2K
Top