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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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  2. jcsd
  3. Mar 22, 2014 #2


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    You can check for why that V/2pi^3 appears here:
    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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