
1) Hamiltonian mechanic 2) Quantum mechanic 3) Theoretical chemistry
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[control theory] This difference is somewhat confusing, nevertheless a specific problem, such as the Brachystochrone problem, can be solved by either method. For details, see the article by Sussmann and Willems. ...
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http://en.wikipedia.org/wiki/Hamiltonian_(control_theory)
[quantum mechanics] In quantum mechanics, the Hamiltonian is the operator corresponding to the total energy of the system. It is usually denoted by H, also Ȟ or Ĥ. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundament...
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http://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

• A mathematical function that can be used systematically and with great generality to generate the equations of motion of a dynamic system. The Hamiltonian is equivalent in many cases to the sum of the kinetic energy and potential energy of a system expressed in terms of the system's coordinat...
Found on
http://www.daviddarling.info/encyclopedia/H/Hamiltonian.html
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