Wave mechanics of a free particle

George Paget Thomson

Nicolae Mazilu, Maricel Agop, Ioan Mercheş

This concluding chapter of the book presents some key concepts discussed in the book. Scale Relativity Theory (SRT) is a necessary theory of interpretation. With the advent of wave mechanics, the interpretation has been established as a necessity within the core of physics itself. Even if it is possible to eliminate the wave mechanics from our knowledge, the interpretation still cannot be eliminated. The fundamental feature of the concept of interpretation turns out to be the idea of freedom of particles: the wave function is referring to an ensemble of free particles. The approach of the interpretation concept, whereby the wave function is interpreted by ensembles of Hertz free particles, and the potential of forces describes implicitly these forces, is a natural situation according to the very idea of quantization of the wave mechanics. In hindsight, this interpretation warrants the Laurent Nottale’s approach of SRT by geodesic motions description of a fractal fluid.

N. F. Mott, Milton E. Rose

Frederick T. Wall

Discrete wave mechanics is formulated for particles in one-dimensional systems by use of a simple finite difference equation. The solutions involve wave vectors (instead of wave functions) as well as a newly defined "wave vector energy." In the limit, as c --> infinity, the treatment reduces to that of Schrödinger's wave mechanics. Specific calculations are made for completely free particles as well as for particles confined to a one-dimensional box. The results exhibit a striking compatibility with relativistic considerations. The wave vectors show properties that can be identified with particles and anti-particles-each possess identical probability distributions with energies that add up to zero.

Shabnam Siddiqui

This chapter discusses several applications of the formalism of theory of quantum mechanics. The time-independent Schrodinger equation is applied to understand simple quantum systems such as a free particle, a particle in an infinite square well, step potentials, potential barrier and finite square well. The chapter deals with the simplest case, a free particle. It is the most elementary application of the formalism. A free particle means that no forces are acting on the particle, and hence, there is no interaction between the particle and its environment. According to classical mechanics, a free particle moves with a constant velocity along a straight line. The energy of the wave associated with the free quantum particle is same as that of the classical free particle. The chapter describes a quantum free particle as a wave packet traveling in space and time. It discusses a quantum particle under the influence of a force.

N. F. Mott, Ian Naismith Sneddon