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Article

Hamilton Equations, Commutator, and Energy Conservation

1
College of Engineering, Purdue University, West Lafayette, IN 47907, USA
2
College of Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA
3
Physics Department, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA
4
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310058, China
*
Author to whom correspondence should be addressed.
Based on the talk presented at the 40th Progress In Electromagnetics Research Symposium (PIERS, Toyama, Japan, 1–4 August 2018).
Quantum Rep. 2019, 1(2), 295-303; https://doi.org/10.3390/quantum1020027
Received: 12 September 2019 / Revised: 1 December 2019 / Accepted: 3 December 2019 / Published: 9 December 2019
We show that the classical Hamilton equations of motion can be derived from the energy conservation condition. A similar argument is shown to carry to the quantum formulation of Hamiltonian dynamics. Hence, showing a striking similarity between the quantum formulation and the classical formulation. Furthermore, it is shown that the fundamental commutator can be derived from the Heisenberg equations of motion and the quantum Hamilton equations of motion. Also, that the Heisenberg equations of motion can be derived from the Schrödinger equation for the quantum state, which is the fundamental postulate. These results are shown to have important bearing for deriving the quantum Maxwell’s equations. View Full-Text
Keywords: quantum mechanics; commutator relations; Heisenberg picture quantum mechanics; commutator relations; Heisenberg picture
MDPI and ACS Style

Chew, W.C.; Liu, A.Y.; Salazar-Lazaro, C.; Na, D.-Y.; Sha, W.E.I. Hamilton Equations, Commutator, and Energy Conservation. Quantum Rep. 2019, 1, 295-303. https://doi.org/10.3390/quantum1020027

AMA Style

Chew WC, Liu AY, Salazar-Lazaro C, Na D-Y, Sha WEI. Hamilton Equations, Commutator, and Energy Conservation. Quantum Reports. 2019; 1(2):295-303. https://doi.org/10.3390/quantum1020027

Chicago/Turabian Style

Chew, Weng C., Aiyin Y. Liu, Carlos Salazar-Lazaro, Dong-Yeop Na, and Wei E.I. Sha. 2019. "Hamilton Equations, Commutator, and Energy Conservation" Quantum Reports 1, no. 2: 295-303. https://doi.org/10.3390/quantum1020027

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