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Transition Rates / Squared Dirac Delta

  1. Mar 22, 2014 #1
    I am not understanding something from my textbook. This is related to Fermi's Golden rule. It's about what happens when the matrix element of the perturbation [itex]H'[/itex] ends up being a Dirac delta for chosen normalization. Here is Fermi's Golden rule.
    [itex]\Gamma_{ba} = 2\pi \left|\langle b \mid H'\mid a \rangle \right|^2 \delta\left(\omega_a - \omega_b \right) [/itex]
    I don't understand what is meant by "...is the decay rate into all the particles in the volume [itex]V[/itex]. The number of particles in [itex]V[/itex] is [itex]V/(2\pi)^3[/itex]."
     

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  3. Mar 22, 2014 #2

    ChrisVer

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    You can check for why that V/2pi^3 appears here:
    http://www2.ph.ed.ac.uk/~gja/qp/qp12.pdf
    in the 2nd page.
    In fact since in the momentum space the volume is such as he proves it, the number of particles will be the inverse.
     
  4. Mar 22, 2014 #3

    Meir Achuz

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    [tex]\delta({\bf 0})=V/(2\pi)^3[/tex].
     
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