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Closure rule

  1. Oct 11, 2008 #1
    hey
    Im having problem about closure rule
    can anyone explain the closure rule?
    why does it gives one

    mads
     
  2. jcsd
  3. Oct 12, 2008 #2

    olgranpappy

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    you might want to elaborate on your question a little more... but an equally vague answer would be that the closure rule gives one because the states form a complete set.
     
  4. Oct 12, 2008 #3
    well it's stated as this
    [tex]\sum{|r><r|}=I[/tex]
    I do understand a lot of QM but why is it gived as a summed product. how does bracket notation work in the sense?. what is the difference to [tex]\sum{<r|r>}[/tex]. I cant picture it in my head.
     
  5. Oct 12, 2008 #4

    olgranpappy

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    sorry. I tried to write a more complete post using TeX... but the forums are not letting me post it.

    So... briefly:

    <a|b> is an inner product in Dirac's notation. A number.

    |a><b| is an "outer product". This is an operator (called a "dyadic"). It acts on states. For example,
    the action on a state |c> is to produce a ket proportional to |a>, namely |a><b|c>.

    To prove the expression for a complete set write an arbitraty ket |psi> in terms of a sum over the complete set {|r>}. The coefficient of each term in the sum can be rewritten in terms of the inner product of |psi> with |r>. Rearranging and noting that psi is arbitrary gives I=sum_r |r><r|
     
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