I am currently dealing with $1$ or at most $2$-dimensional Schrödinger operators on compact domains. A classical result of spectral theory is the Weyl approximations [for this operator](http://en.wikipedia.org/wiki/Weyl_law#Generalizations)
$H = -\Delta +V$. Now I was wondering whether there are any more recent overviews for asymptotic approximations available? Unfortunately, the wikipedia article does not link to any direct reference and as I am not an expert in this field, I am not quite sure whether good overview articles exist? 


$V$ shall be a continuous function.



Asymptotic behavior of Schrödinger operators
This review from 2007 contains a very extensive reference list.


[Some bound state problems in quantum mechanics](http://www.math.uiuc.edu/~dirk/preprints/simonfest8.pdf) (Dirk Hundertmark).


*“Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday” (F. Gesztesy et al., eds.), pp. 463–496, Proc. Symp. Pure Math., 76.1, American Mathematical Society, Providence, RI, 2007.*



> 
> We give a review of semi-classical estimates for bound states and
>  their eigenvalues for Schrödinger operators. Motivated by the
>  classical results, we discuss their recent improvements for single
>  particle Schrödinger operators as well as some applications of these
>  semi-classical bounds to multi-particle systems, in particular, large
>  atoms and the stability of matter.
> 
> 
> 


