We provide a simple proof of (a modification of) Kato's theorem on the Holder continuity of wave packets in N-body quantum systems. Using this method of proof and recent results of O'Connor, we prove a pointwise bound on discrete eigenfunctions of energy E. Here E>O, a:=2 (mass of the system) [dist (E, o",)] and 1x1 is the radius of gyration. . Introduction. In 1957, T... Kato published a beautiful paper [2] which has not received the attention it deserves. Our secondary goal in this note is to

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... provide a simple proof of Kato's result on the Holder continuity of "wave packets" (i.e. vectors in Cm(H))for N-body quantum systems on R~.~-with two body potentials. Our proof of this fact, which appears in 92, uses the basic elements of Kato's proof, especially an Lp-bootstrap; but by working in momentum space instead of configuration space, we avoid the use of modified fundamental solutions and the only Lp estimates we will need are Holder's and Young's inequalities. Our interest in Kato's paper was aroused by, and our major goal is related to, recent work of R. Ahlrichs [I] on the exponential falloff of discrete eigenfunctions of atomic systems. On physical grounds, one expects such an eigenfunction Y to behave more or less like exp (-aolxl) as Ix]-+cc where 1x1 is the radius of gyration of the system (see 93) and where a, is a simple function of the masses of particles and the distance of the eigenvalue from the essential spectrum, (see 93 for an explicit formula). Ahlrichs proves that exp(alxl)Y E L V o r any a<ao. He then uses Kato's result to prove that Y obeys a pointwise bound where b<aao with a an explicit constant smaller than 1. One expects a bound of the form ( I ) to hold for all b<a, and it is this result which is our