Proof of an entropy conjecture of Wehrl

Wehrl has proposed a new definition of classical entropy,S, in terms of coherent states and conjectured thatS1. A proof of this is given. We discuss the analogous problem for Bloch coherent spin states, but in this case the conjecture is still open. An inequality for the entropy of convolutions is also given.Work partially supported by US National Science Foundation grant MCS 75-21684 A02