What is the correct formula for the density of states in 2D for normal atoms?

[tanaygupta2000]

Homework Statement

Density of states in two dimensions in statistical mechanics

Relevant Equations

g(p)dp = 2πApdp/h^2

For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons). I am getting the 2D density of states formula as :- g(p)dp = 2πApdp/h^2

I think this is the formula for normal particles, and so for photons I need to multiply it with 2. But various articles on the internet say that it will be 4πApdp/h^2 instead of 2πApdp/h^2 for normal atoms.

Which formula is correct for normal atoms?

 

[anuttarasammyak]

https://en.wikipedia.org/wiki/Density_of_states seems to coincide with your relevant equation.

 

[tanaygupta2000]

Okay, I got to know that the 2D density of states for a monoatomic gas is given by:
g(ϵ)dϵ = (2πmA)/h^2 dϵ

 

[DrClaude]

Okay, I got to know that the 2D density of states for a monoatomic gas is given by:
g(ϵ)dϵ = (2πmA)/h^2 dϵ

That is correct. So the correct density of momentum states for monatomic atoms in 2D is the one you had in the OP:
$$
g(p) dp = \frac{2 \pi A}{h^2} p dp
$$
which you multiply by 2 for photons.