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Why is there a sum being used

  1. Oct 22, 2013 #1
    I am reading the paper on the Casimir effect and they measure the space in between the plates using a sum and the energy of the vacuum without the plates using an intregal. Why do they use the sum and intregal, should they be switched.
     

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  2. jcsd
  3. Oct 22, 2013 #2
    Between the plates, only modes with a discrete set of frequencies exist, so we sum over them. Without the plates, a continuum of frequencies is possible (all frequencies are allowed) so the sum becomes an integral.
     
  4. Oct 22, 2013 #3
    Thank you sir
     
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