On the Principles of Elementary Quantum Mechanics

H.J. Groenewold

Hilbrand Johannes Groenewold

Nikolay Leonidovich Chuprikov

On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three quite feasible innovations in quantum mechanics (QM): (1) at the conceptual level, QM must treat a pure time-dependent one-particle state to involve two or more macroscopically distinct alternatives for a particle as a pure {\it combined} one - the intermediate link between a pure {\it elementary} state (indecomposable into macroscopically distinct parts) and statistical mixture; (2) at the mathematical level, QM must provide the presentation of the pure time-dependent combined state as a coherent superposition of macroscopically distinct elementary states (MDESs); (3) at the experimental level, QM must provide for such states two types of measurements - those for observing the interference pattern resulting from the joint action of MDESs, and non-demolishing 'which-way' measurements for scanning the individual properties of MDESs.

Hironari Yamada

Author has given an interpretation of quantum mechanics in totally new approach named Dialogue Principle. Author point out how similar is the living phenomena and human behavior to the movement of elementary particles, if we agree with that the wave function implies the existing probability of elementary particles in the topological space. In the dialogue principle, the reasons for this similarity is explained by introducing common concept “character” and “will” among living specimens as well as elementary particles. Author describes that “will” is the origin of all strange behavior among elementary particles as well as human beings. “Will” is the subject of 21st Century to be studied scientifically. Author proposes that the concept of “will” should be added to the base of modern science to gives unified understanding of all existence including elementary particles, human beings, and universe. In this paper the digest of the dialogue principle is given, and approaches to the meaning of life by the philosophy of quantum mechanics.

Derek F. Lawden, Garrison Sposito

Gordon Baym

These lecture notes comprise a three-semester graduate course in quantum mechanics at the University of Illinois. There are a number of texts which present the basic topics very well; but since a fair quantity of the material discussed in my course was not available to the students in elementary quantum mechanics books, I was asked to prepare written notes. In retrospect these lecture notes seemed sufficiently interesting to warrant their publication in this format. The notes, presented here in slightly revised form, consitutute a self-contained course in quantum mechanics from first principles to elementary and relativistic one-particle mechanics. Prerequisite to reading these notes is some familiarity with elementary quantum mechanics, at least at the undergraduate level. Preferably the reader should already have met the uncertainty principle and the concept of a wave function. Prerequisites also include sufficient acquaintance with complex cariables to be able to do simple contour integrals and to understand words such as "poles" and "branch cuts." An elementary knowledge of Fourier transforms and series is necessary. I also assume an awareness of classical electrodynamics.