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Completeness of basis in quantum mechanics

  1. Oct 2, 2014 #1
    In a QM course,
    I learn that an operator can be represented by basis vectors
    If the basis vector is complete, the following relation holds
    There exist coefficient Mij such that
    Sigma Mij |i > < j|. = I , |i> is the basis! and I is the identity matrix

    But isn't that in linear algebra
    We call the set of basis is complete when
    Any vector can be expressed into their linear combination

    I wonder why here we seems have 2 definition of completeness
     
  2. jcsd
  3. Oct 2, 2014 #2
    I recommend reading of Sakurai's Book on QM - read the introductory chapters.
     
  4. Oct 2, 2014 #3

    BvU

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    There is only one definition if the two renderings are equivalent, right ? And they are equivalent!
     
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