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

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).

If you are only interessted in the Schrödinger Operator, maybe the book Semi-Classical Analysis for the Schrödinger Operator and Applications 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.

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

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).

If you are only interessted in the Schrödinger Operator, maybe the book Semi-Classical Analysis for the Schrödinger Operator and Applications 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.