Page "Diagonalizable matrix" Paragraph 105
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In quantum mechanical and quantum chemical computations matrix diagonalization is one of the most frequently applied numerical processes.
The basic reason is that the time-independent Schrödinger equation is an eigenvalue equation, albeit in most of the physical situations on an infinite dimensional space ( a Hilbert space ).
A very common approximation is to truncate Hilbert space to finite dimension, after which the Schrödinger equation can be formulated as an eigenvalue problem of a real symmetric, or complex Hermitian, matrix.
Formally this approximation is founded on the variational principle, valid for Hamiltonians that are bounded from below.
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