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## Main Question or Discussion Point

In my particles course, it says we will use Fermi's golden rule to work out rates.

FGR is:

Γ=2π|M

For the case of non-relativistic phase space, my notes say the density of states can be found as follows (pretty much word for word):

Apply boundary conditions

Wave-function vanishing at box boundaries ⇒ quantised particle momenta

Volume of single state in momentum space:

(2π/a)

Normalizing to one particle/unit volume gives:

Number of states in element d

[itex]dn=\frac{d^{3}p}{\frac{(2\pi)^3}{V}} \frac{1}{V}[/itex]

Then a bit more algebra to get some result

I've normally only seen density of states come into the picture for systems with periodic boundary conditions. If we're talking about particle physics and the rate of a collision producing another particle, I don't see why the wavefunction should vanish at the boundary of some box. The only constraint is that the wavefunction should be 0 at infinity. Surely there should be a continuous spectrum of possible wavevectors for the final particle?

Thanks

FGR is:

Γ=2π|M

_{fi}|ρFor the case of non-relativistic phase space, my notes say the density of states can be found as follows (pretty much word for word):

Apply boundary conditions

Wave-function vanishing at box boundaries ⇒ quantised particle momenta

Volume of single state in momentum space:

(2π/a)

^{3}= (2π)^{3}/VNormalizing to one particle/unit volume gives:

Number of states in element d

^{3}p=dp_{x}dp_{y}dp_{z}[itex]dn=\frac{d^{3}p}{\frac{(2\pi)^3}{V}} \frac{1}{V}[/itex]

Then a bit more algebra to get some result

I've normally only seen density of states come into the picture for systems with periodic boundary conditions. If we're talking about particle physics and the rate of a collision producing another particle, I don't see why the wavefunction should vanish at the boundary of some box. The only constraint is that the wavefunction should be 0 at infinity. Surely there should be a continuous spectrum of possible wavevectors for the final particle?

Thanks