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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Coupled Classical Oscillators

Pp. 247-250 (4)

Peter Enders

Abstract

Since this part Field Quantization as Selection Problem attempts to carry over the quantization of point-mechanical systems to that of classical fields, it begins with a chapter about coupled harmonic oscillators being the classical basis of phonons, the quantum particles of sound. After establishing the Newtonian equations of motion, the eigenmodes are calculated as a Toeplitz eigenvalue problem. Finally, the canonical momentum and the Hamiltonian are provided.

Keywords:

Canonical momentum, Coupled classical oscillators, Eigenmodes, Hamiltonian, Quantization, Toeplitz eigenvalue problem.

Affiliation:

Taraz State Pedagogical University, Kazakhstan.