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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Possible and Impossible (Momentum) Configurations

Pp. 74-77 (4)

Peter Enders

Abstract

This chapter prepares a smooth way from Eulerian classical mechanics to quantum mechanics. Starting from Helmholtz’s foundation of the energy conservation law using Leibniz’s theorem as described in the foregoing Chapter 2, the configurations a system can (cannot) assume in a given stationary state are explored. The following constraints are taken into account: Newton-Euler’s exclusion principle, d’Alembertian constraints and constraints imposed by conservation laws. The set of possible and impossible momentum configurations is also considered, using Nemorarius’ theorem of the foregoing chapter.

Keywords:

d’Alembertian constraints, Conservation laws, Helmholtz, Hodograph, Impossible configurations, Impossible momentum configurations, Leibniz’s theorem, Momentum configuration space, Nemorarius’ theorem, Newton-Euler’s exclusion principle, Possible configurations, Possible momentum configurations, Schütz, State, State function, Stationary state.

Affiliation:

Taraz State Pedagogical University, Kazakhstan.