An algebra of pseudodifferential operators and the asymptotics of quantum mechanics

AbstractWe discuss in detail the regularity properties of a class of pseudodifferential operators on Rl introduced by Grossmann, Loupias, and Stein, which are more regular and more symmetrical than usual pseudodifferential operators. Those operators that are self-adjoint form a suitable class of smooth observables for a nonrelativistic quantum theory. If their symbols are allowed to depend smoothly upon Planck's constant h̵, those operators provide the framework for regular asymptotics expansions as h̵ → 0 of quantum mechanics around classical mechanics