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How to represent operator in matrix form

  1. Sep 20, 2011 #1
    I'm given some arbitrary operator call it O, how do I represent it in general matrix form while it still preserves the properties of the operator.

    ex. if operator is hermitian how to i represent a most general matrix representation so it preserves properties of a hermitian matrix.
  2. jcsd
  3. Sep 21, 2011 #2


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    You need a basis of Hilbert space, [itex]\{|n \rangle \}_{n \in \mathbb{N}}[/itex], e.g., the harmonic-oscillator-energy eigen states. Then the matrix elements of an arbitrary operator, [itex]\hat{O}[/itex] are given by

    [tex]O_{jk}=\langle j|\hat{O} k \rangle.[/tex]

    It's easy to verify that this is an Hermitean matrix, if [itex]\hat{O}[/itex], is selfadjoined.
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