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


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.


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.


Taraz State Pedagogical University, Kazakhstan.