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Resolution of the Identity

  1. Oct 8, 2011 #1
    How do I prove that

    Ʃ\ket{ei} \bra{ei} = I
     
  2. jcsd
  3. Oct 8, 2011 #2

    strangerep

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    It depends on the context, and precisely what your [itex]e_i[/itex] stand for.

    As a general suggestion, start by looking up the "spectral theorem" in a linear algebra textbook. (Wikipedia gives an overview, though not the details.)
     
  4. Oct 8, 2011 #3
    [itex]e_i[/itex] refers to a finite orthonormal basis
     
  5. Oct 8, 2011 #4

    strangerep

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    OK, so if you write out how an arbitrary vector [itex]\psi[/itex] is expressed in terms of that orthonormal basis, the desired answer should then follow almost immediately.
     
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