Another reference is Helffer and several Coauthors (Sjöstrand, Nier, Klein, Garyard, ...) using the Witten-Laplace approach.

An introduction is given in the book
[Semiclassical analysis, Witten Laplacians, and statistical mechanics][1]

Later sharp asymptotics for the low lying spectra in the case where $V$ consists of several minima were obtained. Some lecture note on this topic [Low lying eigenvalues of Witten Laplacians and metastability (after Helffer-Klein-Nier and Helffer-Nier)][2]. 

If you are only interessted in the Schrödinger Operator, maybe the book [Semi-Classical Analysis for the Schrödinger Operator and Applications][3] is the most interesting for you. There are also lecture notes available [Semiclassical Analysis for Schrödinger Operators, Laplace Integrals and Transfer Operators in large dimension: an introduction.][4]


  [1]: http://books.google.de/books?id=43vAd5KoEkUC
  [2]: http://www.math.kth.se/spect/preprints04_05/Helf3.pdf
  [3]: http://www.springerlink.com/content/978-3-540-50076-6
  [4]: http://www.math.u-psud.fr/~helffer/CoursDEA95main.ps