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This article deals with isotropic elastic materials which possess a strain energy function. For such materials the strain energy of a material point is given, of course, by a symmetric function σ of the principal stretches v 1 , v 2 , v 3 at that point. It is known that a necessary condition to...
Two conjectures made in a previous paper are proved. A further remark is made concerning the largest eigenvalue of the reduced density matrices.
The potential‐scattering model is discussed from the point of view of analyticity properties of the scattering amplitude. Dynamical schemes based on the Mandelstam representation and the use of Regge poles are reviewed. Consequences for strong interaction physics are also briefly reviewed.
An ideal Heisenberg model of a ferromagnet for spin ½ 1 2 is studied by considering the model in terms of a spin‐deviation lattice gas. Utilizing the general methods of Yang and Lee, a binary kernel function is obtained in terms of which the thermodynamic properties of the lattice gas can be...
A new method is presented for obtaining irreversible equations describing the approach to equilibrium in systems of many particles. The basic idea is the removal of secular terms arising in a perturbation expansion by the technique used in nonlinear mechanics. The irreversible equations then...
A simple modification of a method introduced by R. Bellman is proposed, which under certain circumstances produces both upper and lower bounds for the solution of the Riccati equation. An application to scattering theory is suggested.
Elastic and inelastic collisions in the Lee model are treated in a dressed‐particle picture. The procedure by which the renormalization constant Z disappears from the integral equations for the transition matrix is studied in detail. A new procedure is given for obtaining the exact transition...
The partial wave series for a relativistic charged spinless particle is not uniformly convergent and is difficult to evaluate numerically in the forward direction. The singularity in the scattering amplitude at the forward direction which leads to this nonuniform convergence is separated and...
We consider two harmonic oscillators, coupled during a finite time. Initial and final states can be defined unambiguously, and if the duration of the coupling is sufficiently short, the S matrix can be computed explicitly. The coupling gx 2 y is investigated in detail, for complex values of g ....
Variational principles for obtaining the eigensolutions ψ i of the equation ∇ 2 ψ − ψ + ψ 3 = 0 ∇ 2 ψ − ψ + ψ 3 = 0 are developed. Variational solutions to the first two spherically symmetric eigenstates are obtained. Variational solutions of odd parity are also obtained.
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