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We prove a mathematical conjecture by Dyson which he used in a study of the statistical distribution of energy levels in complex nuclei.
An exact solution is given for the partial differential equation y t t = 1 + ϵ y x α y x x , which describes the standing vibrations of a finite, continuous, and nonlinear string. The nonlinearity studied, 1 + ϵ y x α , was motivated by the work of Fermi, Pasta, and Ulam (1955), where they...
The problem of determining a solution of the Einstein field equations for the gravitational field from data set on a pair of intersecting characteristic (that is, null) hypersurfaces and on their intersection Σ is considered. It is shown that by giving the conformal inner metric of each...
The phase shift formulas for the wave and scattering operators in the potential scattering of a single nonrelativistic particle are proved under weaker assumptions on the potential than the one used previously by Green and Lanford.
Thermodynamical functions for classical and quantum systems are expressed in terms of the one‐particle density n 1 and the two‐particle correlation matrix C 12 (or quantities in direct relation to them). Use is made of topological relations valid for the diagram representations of the grand...
The most general continuous time‐dependent evolution of a physical system is represented by a continuous one‐parameter semi‐group of linear mappings of density operators to density operators. It is shown that if these dynamical mappings form a group they can be represented by a group of...
The S matrix associated with a central potential is shown to be meromorphic in the energy and angular momentum variables under very broad conditions. The domain of meromorphy contains the product of a domain in the energy variable by a domain in the angular variable. The former (latter) domain...
Maxwell's equations are formulated in a number of different representations: (a) As a single four‐component spinor equation whose transformation properties are almost identical with those of the Dirac equation. (b) As a pair of uncoupled two‐component spinor equations, in two different...
The partitioning technique for solving secular equations is briefly reviewed. It is then reformulated in terms of an operator language in order to permit a discussion of the various methods of solving the Schrödinger equation. The total space is divided into two parts by means of a...
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