An Outline of Wave Mechanics.

Edwin Plimpton Adams, H.F. Biggs

Helmut Rechenberg

On the occasion of the 100th birthday of Erwin Schrodinger, an outline of his life and work is presented, together with an analysis of the steps that led him to wave mechanics.

P. J. E. Peebles

This chapter develops the wave mechanics formalism. The emphasis here is on symmetries and conservation laws: parity, linear and angular momentum, and the electromagnetic interaction. The only specific physical application is the completion of the study of an isolated hydrogen atom, with some discussion of the motion of a particle in a magnetic field. The chapter also outlines the general assumptions of quantum wave mechanics, which may be summarized as follows: the state of a physical system is represented by a wave function and each measurable attribute of the system is represented by a linear self-adjoint operator in the space of functions. To apply these general assumptions to a given physical system, one must give a specific prescription for the observables and their algebra, and one must adopt a definite form for the Hamiltonians as a function of the observables.

Walter Heinrich Heitler, Edward L. Hill

Helmut J. Fischbeck, Kurt H. Fischbeck

Daniel D. Pollock

The approach is to start with some of the elementary ideas of classical mechanics and to translate these concepts to their equivalents in quantum mechanics. This will be done by changing the classical components of the total energy of particle into their quantum mechanical equivalents and arriving at the Schrodinger equation. The conjugate variables, position and momentum, in the Hamiltonian functions can be determined precisely for classical mechanical applications. This chapter deals with the Schrodinger model of the behavior of single electrons as affected by potential wells. The wave mechanic approach is extended to provide an outline of the interactions of many electrons with nuclei. In terms of the Pauli exclusion principle, the four quantum numbers of the electron states must be different. As additional electrons are added, the states available for occupation can be filled only according to the rules governing the quantum numbers.