Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach

Coupled Classical Oscillators

Author(s): Peter Enders

Pp: 247-250 (4)

DOI: 10.2174/9781681084497119010023

* (Excluding Mailing and Handling)


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.

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