Introduction

Abstract

The structure of quantum mechanics differs startlingly from that of the classical theory. In volume I we learned that in classical mechanics the observables form an algebra of functions on phase space (p and q), and states are probability measures on phase space. The time-evolution is determined by a Hamiltonian vector field. It would be reasonable to expect that atomic physics would distort the vector field somewhat, or even destroy its Hamiltonian structure; but in fact the break it makes with classical concepts is much more drastic. The algebra of observables is no longer commutative. Instead, position and momentum satisfy the famous commutation relations,

$$qp - pq = i\hbar .$$

(1.1)