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Annals of Physics

Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

Ciann‐Dong Yang

Published Sep 9, 2006• 63 citations
Publisher
DOI
10.1016/j.aop.2006.07.008

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The Hamilton approach to classical dynamics is extended to incorporate quantum effects. Quantization of the Hamilton equations of motion results in a hierarchy of equations that are equivalent to quantum mechanics in the Heisenberg form. Closure of the hierarchy gives approximations to the exact quantum dynamics. A specific dynamics algorithm is presented and tested against model applications that exhibit tunneling and zero point motion effects. The quantized Hamilton approach is found accurate, consistent, flexible, and computationally very efficient.