Contribution to the wave mechanics of the particle of maximum spin 1.

E. Corinaldesi, Franco Strocchi

Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat

Jos� Vassalo Pereira

Juho Leppäkangas

We employ the maximum entropy principle, in the context of statistical inference by impersonal physical interactions, together with the experimental position-momentum uncertainty phenomenon to construct the general wave mechanical static state of a single, interacting mass particle with no internal degrees of freedom. Subsequently, this first principle approach allows to derive via Newtonian mechanics the dynamical equation of motion in the realm of non-relativistic wave mechanics, i.e., the Schrodinger equation.

Gérard Petiau

Alessandro Bressan

O. K. Rice

In the recent theory of radioactive decay, and also, as is shown, in the theory of dissociation of a diatomic molecule by the acquisition of rotational energy, there occurs a potential energy curve which has the following shape, as we go, say, from left to right. At the left the potential energy is very high, it then comes down to a minimum, increases to a maximum, and again falls off to an asymptotic value. The problems connected with such a curve are of two types. First, we may be given a particle in the region near the minimum, in an energy level which lies below the maximum, and wish to find the chance that it appear by a quantum mechanical process in the region on the other side of the maximum. Second, we wish to find how the "discrete states" in the neighborhood of the minimum are "broadened" by the continuum on the other side of the maximum. To solve these problems we first find the stationary eigenfunctions. By means of them the width and shape of the "broadened discrete levels" are found immediately. We then use these eigenfunctions to set up a wave packet, or, rather, we show how nature may set up a wave packet, which enables us to solve the first of the problems mentioned. The result justifies the use of complex eigenvalues for the solution of the problem.