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- Thread starter matqkks
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- Jan 26, 2012

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You can't do better than quantum mechanics and Hilbert space, which is a particular kind of inner product space. If you look at the hydrogen atom, for example, the Schrodinger equation is an eigenvalue problem. The eigenvectors are functions that live in a Hilbert space. You can use the Gram-Schmidt process to reduce the eigenvectors to an orthonormal basis, which is probably the most useful kind of basis. The Gram-Schmidt process makes use of the inner product extensively.