# A general effective Hamiltonian method

### André Martinez

Università di Bologna, Italy

## Abstract

We perform a general reduction scheme that can be applied in particular to the spectral study of operators of the type $P=P(x,y,hD_x,D_y)$ as $h$ tends to zero. This scheme permits to reduce the study of $P$ to the one of a semiclassical matrix operator of the type $A=A(x,hD_x)$. Here, for any fixed $(x,\xi )\in\R^n$, the eigenvalues of the principal symbol $a(x,\xi )$ of $A$ are eigenvalues of the operator $P(x,y,\xi ,D_y)$.

## Cite this article

André Martinez, A general effective Hamiltonian method. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 269–277

DOI 10.4171/RLM/494