Overlap matrix

The overlap matrix is a square matrix used in quantum chemistry, to describe the inter-relationship of a set of basis vectors of a quantum system. In particular, if the vectors are orthogonal to one another, the overlap matrix will be diagonal. In addition, if the basis vectors form an orthonormal set, the overlap matrix will be the identity matrix. The overlap matrix is always n×n, where n is the number of basis functions used. It is a kind of Gramian matrix.

Related Topics:
Square matrix - Quantum chemistry - Basis vector - Quantum - Orthogonal - Orthonormal - Identity matrix - Gramian matrix

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In general, the overlap matrix is defined as:

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:mathbf{S}_{jk}=left langle b_j|b_k ight angle=int Psi_j^* Psi_k d au

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where

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:left |b_j ight angle

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is the j-th basis ket (vector), and

Related Topics:
Ket - Vector

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:Psi_j

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is the j-th wavefunction, defined as

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:Psi_j(x)=left langle x | b_j ight angle.

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