About One Newell's Result and the Quantum Mechanical Check of the Microcanonical Distribution

摘要

G.F. Newell succeeded to prove for the eigenfunctions PSIsub(n)(x) of the k-dimensional Schroedinger equation (- delta sub(k)+q(xsub(1), xsub(2)..., xsub(k))-lambdasub(n))PSIsub(n)(x)=0, integral /PSIsup(2)(x)/dsup(k)x=1, q(x)>=0, q(x) implies +infinity at x implies infinity the asymptotic relation (lambda implies +infinity) sigma sub(lambdasub(n)<=lambda)PHIsub(n)(x)sup(2)=(lambda- q(x))sup(k/2)x(1+0(1)/(4 pi )sup(k/2)GITA(1+k/2)). The intent is to attract attention to the fact that the equation is a simple consequence of the classical microcanonical distribution. Thus the Newell result allows one to check the microcanonical distribution hypothesis by the methods of quantum mechanics. (Atomindex citation 14:718056)