The Development of Elementary Quantum Theory

Ronald F. Peierls

Mehdi Hage-Hassan

Quantum mechanics originates from the study of the spectrum of hydrogen atom and the black body radiation and the development of this theory has been very successful for the study of atoms, the nucleus and the classification of elementary particles using SU (3) group. But the course of quantum mechanics in the second year should be revised to take account of these developments not only in terms of program but also from an educational point of view, especially for students of mathematical orientation. In this work we give an idea about the origin of quantum mechanics and we summarize the Schrodinger, the Dirac formalisms of quantum mechanic and the path integral. After exposing the Dirac's method of the oscillator we treat the Schwinger's approach of angular momentum. We present the theory of the central potential, the Quarks model and the classification: of chemical elements and elementary particles. We present a summary of the approaches of group theory. We present the theory of SU (3) and the decomposition of tensor product of SU (3). To take account of level of students we use in the applications our generating function method for its simplicity.

Ulf Leonhardt, T. Kiss, Patrik Öhberg

Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the non-condensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to a sonic white hole and find that the spectrum of unstable modes is intrinsically discrete.

Paul A. Flowers, Edward J. Neth, William R. Robinson +2 more

H. Capellmann

Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contributors. The fundamental laws of Quantum Theory derived by Max Born and Pascual Jordan may mathematically be represented in many different ways, and particular emphasis is given to the distinction between physical content and mathematical representation.

David V. George