formalisms:hamiltonian_formalism
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formalisms:hamiltonian_formalism [2018/05/04 09:53] jakobadmin ↷ Links adapted because of a move operation |
formalisms:hamiltonian_formalism [2018/05/05 12:16] jakobadmin [FAQ] |
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| --> How is the Hamiltonian Formalism related to the Newtonian Formalism?# | --> How is the Hamiltonian Formalism related to the Newtonian Formalism?# | ||
| - | <blockquote>"Recall that we derived Hamilton’s equations for a particle moving in a force field $F = -dV/dx$ by writing down the equations of motion in the form $$ m \dot{x} = p , \quad \dot{p} = - \frac{\partial V}{\partial x} .$$ The observant reader will have noticed that these two equations are just one way to express Newton’s second law. More generally for a system of N point-like particles moving in three-dimensional physical space, Newton’s second law would be $$ m \dot{x_j} = p_j , \quad \dot{p}_j = - \frac{\partial V}{\partial x_j} .$$" <cite>The symplectic egg in classical and quantum mechanics by Maurice A. de Gosson</cite></blockquote> | + | <blockquote>Recall that we derived Hamilton’s equations for a particle moving in a force field $F = -dV/dx$ by writing down the equations of motion in the form $$ m \dot{x} = p , \quad \dot{p} = - \frac{\partial V}{\partial x} .$$ The observant reader will have noticed that these two equations are just one way to express Newton’s second law. More generally for a system of N point-like particles moving in three-dimensional physical space, Newton’s second law would be $$ m \dot{x_j} = p_j , \quad \dot{p}_j = - \frac{\partial V}{\partial x_j} .$$ <cite>The symplectic egg in classical and quantum mechanics by Maurice A. de Gosson</cite></blockquote> |
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formalisms/hamiltonian_formalism.txt · Last modified: 2023/04/02 03:34 by edi
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