Classical Mechanics and Quantum Mechanics:  An Historic-Axiomatic Approach

Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach

This unique textbook presents a novel, axiomatic pedagogical path from classical to quantum physics. Readers are introduced to the description of classical mechanics, which rests on Euler’s and ...
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Summary and Conclusions

Pp. 271-280 (10)

Peter Enders

Abstract

This chapter summarizes the main results of this book and draws some conclusions. Special attention is paid to the axiomatic basis, i.e., to Schrödinger’s requirements and Hertz’s program, which lead to the novel paradigm of quantization as selection problem (rather than eigenvalue problem). Both ones are realized by means of limiting (Schrödingerian weight) functions, which guarantee the validity of the energy conservation law in the classically forbidden regions of configuration and momentum configuration spaces (e.g, beyond the turning points of classical oscillators). Further topics are the separation of external and internal parameters as initiated by Euler, the differences between classical and quantum wave equations, causality and determinism, hidden variables, symmetry and field quantization.

Keywords:

Axiomatic, Causality, Configuration, Determinism, Euler, External parameters, Field quantization, Hertz’s program, Hidden variables, Internal parameters, Limiting functions, Momentum configuration, Quantization, Schrödinger’s requirements, Symmetry, Trajectory, Wave equation, Weight functions.

Affiliation:

Taraz State Pedagogical University, Kazakhstan.