Rules of probability in quantum mechanics

We show that the quantum mechanical rules for manipulating probabilities follow naturally from standard probability theory. We do this by generalizing a result of Khinchin regarding characteristic functions. From standard probability theory we obtain the methods usually associated with quantum theory; that is, the operator method, eigenvalues, the Born rule, and the fact that only the eigenvalues of the operator have nonzero probability. We discuss the general question as to why quantum mechanics seemingly necessitates different methods than standard probability theory and argue that the quantum mechanical method is much richer in its ability to generate a wide variety of probability distributions which are inaccessibe by way of standard probability theory.It is a pleasure to dedicate this paper to David Bohm in honor of his 70th birthday.This work is supported in part by The City University Research Award Program.     

Dynamics of Ginzburg‐Landau Vortices

(Accepted August 19, 1996)     

Luminescence of the hydrolysis products of Th(IV)

Raising the pH of an aqueous solution of thorium nitrate results in the precipitation of a hydrated thorium oxide. At room temperature this material does not exhibit any emissive properties, but upon cooling to 77 K a strong green luminescence can be observed. The emission spectrum is fairly broad, and is characterized by an emission lifetime of 125 μs. Calcination of the hydrolysis product produces an anhydrous thorium oxide which is not luminescent at any temperature. Through the production of a series of mixed lanthanide/thorium hydrolysis products, it was established that the luminescent species was a clustered thorium compound. Sensitization of Eu(III) emission by the thorium hydrolysis product was observed.     

Measurement of the depolarization rate of positive muons in copper and aluminum

Positive muon spin rotation experiments for polycrystalline Cu and Al from 19K to temperatures near the melting points are reported. At low temperatures, the depolarization associated with localization of the muons at octahedral interstitial sites is seen in Cu, while in A? only slight depolarization is observed below 250K. At high temperatures, no evidence for trapping of positive muons at vacancies in thermal equilibrium is found for either metal. It is concluded that the muons either diffuse too slowly to find vacancies or, if they do find vacancies, are bound too weakly to remain trapped.