Introduction to semi-classical analysis for the Schr¨ odinger operators

Semi-classical correspondence and exact results : the case of the spectra of homogeneous Schrödinger operators [erratum: J.. Semi-classical correspondence and exact results : the

To discuss the high energy regime (in Section 3) and semi-classical regime (in Section 4), we use the close connection between the Dirac operator and Schrbdinger

In the quantum case, we study the spectral problem of the magnetic Laplacian at the semi-classical level, in two-dimensional domains: on a compact Riemannian manifold with boundary

Finally, in Section 5 we con- sider the semi-classical estimates of the distance of a Toeplitz operator to various spaces (self-adjoint operators, constant multiples of the

• For a given interval K, a clever choice of λ makes possible to get a good approximation of the signal in K in the semi-classical regime with a smaller number of eigenvalues.

As in the regular case (elliptic trajectory), we prove, that for an initial wave packets localized in energy, the dynamics follows the classical motion during short time.. Moreover

ON THE SEMI-CLASSICAL ANALYSIS OF THE GROUNDSTATE ENERGY OF THE DIRICHLET PAULI OPERATOR Bernard Helffer, Mikael Sundqvist.. To cite this version: Bernard Helffer,

• In Section 5, we discuss the case of multi-component wave equations: we will discuss first the (non-realistic) case where the source is a white noise, then the semi-classical