Regularity of eigenstates in regular mourre-theory

Our presentation gives an abstract method for proving that eigenstates of a self-adjoint operator H lie in the domain of the conjugate operator A. Conjugation means here that H and A have a positive commutator in the sense of Mourre. The only requirement is the Ck-regularity of H. Regarding integer k, our result is optimal. Using this method, we obtain cutoff-independent bounds and under a boundedness assumption of the multiple commutators we prove analyticity of the eigenstates with respect to exp(-itA). We illustrate the relevance of this method in a physical application.