Schrodinger Wave Mechanics Research Articles

Equations of motion in a non-integer-dimensional space

Equations of motion are derived for a fractional dimensional system of n-spatial coordinates to be used as an effective description of anisotropic and confined systems. An existing measure theoretic approach is extended to multiple variables and different degrees of confinement in orthogonal directions and comparisons are made with the analytic continuation of Gaussian integrals. This is applied to the variational principle, and equations of motion for a field described by a Lagrange density are found. A specific example is looked at in Schrodinger wave mechanics, particularly in three-coordinate systems.

Formalism, Ontology and Methodology in Bohmian Mechanics

The relationship between mathematical formalism, physical interpretation and epistemological appraisal in the practice of physical theorizing is considered in the context of Bohmian mechanics. After laying outthe formal mathematical postulates of thetheory and recovering the historical roots ofthe present debate over the meaning of Bohmianmechanics from the early debate over themeaning of Schrodinger's wave mechanics,several contemporary interpretations of Bohmianmechanics in the literature are discussed andcritiqued with respect to the aim of causalexplanation and an alternative interpretationis proposed. Throughout, the over-arching aimis to exhibit the connections betweenmathematical, ontological and methodologicalquestions in physical theory and to reflect onthe rationality of physical theorizing in lightof the present case.

Principles of quantum mechanics: as applied to chemistry and chemical physics

This text presents a rigorous mathematical account of the principles of quantum mechanics, in particular as applied to chemistry and chemical physics. Applications are used as illustrations of the basic theory. The first two chapters serve as an introduction to quantum theory, although it is assumed that the reader has been exposed to elementary quantum mechanics as part of an undergraduate physical chemistry or atomic physics course. Following a discussion of wave motion leading to Schrodinger's wave mechanics, the postulates of quantum mechanics are presented along with essential mathematical concepts and techniques. The postulates are rigorously applied to the harmonic oscillator, angular momentum, the hydrogen atom, the variation method, perturbation theory, and nuclear motion. Modern theoretical concepts such as hermitian operators, Hilbert space, Dirac notation, and ladder operators are introduced and used throughout. This text is appropriate for beginning graduate students in chemistry, chemical physics, molecular physics and materials science.

On the quantum mechanics of consciousness, with application to anomalous phenomena

Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrodinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantum mechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent molecular bonds, barrier penetration, and quantum statistical collective behavior become useful analogies for representation of a variety of consciousness experiences, both normal and anomalous, and for the design of experiments to study these systematically.

Eigenvalues and Whittaker's Function

AMONG those who are trying to acquire a general acquaintance with Schrodinger's wave-mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem—to determine the eigenvalues and eigenfunctions for the hydrogen atom. I do not think it is generally realised that Schrodinger's differential equation for this problem is one which is fully treated in a standard text-book, Whittaker and Watson's “Modern Analysis”, Chapter xvi. (I quote from the second edition). It would seem that advantage may be taken of this to make the treatment easier for English readers. I realise that the following is only a slight redressing of Schrodinger's method; but I think it will be intelligible to some who have been unable to appreciate the original, and that it gives a useful idea of the genesis of eigenvalues.

The Hydrogen Atom with a Spinning Electron in Wave Mechanics

In this paper it is shown that the Schrodinger wave mechanics, plus the Uhlenbeck-Goudsmit spinning electron, completely represents the fine structure of hydrogen-like spectra.

Wave Mechanics and Classical Mechanics and Electrodynamics

RECENT articles in this journal by Mr. R. H. PC Fowler, Prof. M. Born, and Dr. P. Jordan have dealt with the relation between Schrodinger's wave mechanics and the quantum theory, but it is admitted that they scarcely express the views of Schrodinger himself or those of his predecessor, L. de Broglie. The object of the present article is to give an account of the researches of these two authors from the viewpoint of classical mechanics and electrodynamics, to which they are closely related, both in subject-matter and method. A brief bibliography of their papers, as well as a few by other writers on the same subject, is appended, to which the reader is referred for details, for an outline only of the line of thought can be given in the present article.