Transition Rates / Squared Dirac Delta

In summary, the conversation is about Fermi's Golden rule and the meaning of the term "decay rate" in the equation. The speaker provides a link to a resource explaining the origin of the term and how it relates to the number of particles in a given volume.
  • #1
MisterX
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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
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.
 
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  • #3
[tex]\delta({\bf 0})=V/(2\pi)^3[/tex].
 
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FAQ: Transition Rates / Squared Dirac Delta

What is a transition rate?

A transition rate is a measure of the rate at which a system changes from one state to another. It is commonly used in physics and chemistry to describe the likelihood of a particle or molecule transitioning from one energy level to another.

How is transition rate related to the squared Dirac delta?

The squared Dirac delta function is a mathematical tool used to describe the probability of a particle transitioning from one state to another. The transition rate is proportional to the squared Dirac delta function, which means that the higher the probability of a transition, the higher the transition rate will be.

What factors affect transition rates?

Transition rates can be affected by a variety of factors, including temperature, energy barriers, and the presence of other particles. In general, higher temperatures and lower energy barriers tend to increase transition rates, while the presence of other particles can either increase or decrease transition rates depending on the specific system.

How are transition rates measured?

Transition rates can be measured experimentally using a variety of techniques such as spectroscopy, which involves shining light on a system and measuring the resulting changes in energy levels. Theoretical calculations can also be used to estimate transition rates based on the properties of the system.

What are some real-world applications of transition rates and the squared Dirac delta?

Transition rates and the squared Dirac delta have many practical applications, including in the fields of quantum mechanics, chemical kinetics, and materials science. They are also used in the design of electronic devices and in understanding processes such as radioactive decay and chemical reactions.

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