Results 141 to 150 of about 1,595,440 (180)
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2012
We have repeatedly emphasized that determining the explicit solutions of Hamiltonian equations is a task beyond the capabilities of mathematics. This situation justifies all attempts to obtain information about these solutions. For instance, a knowledge of the first integrals allows us to localize the dynamical trajectories in the phase space M 2n ...
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We have repeatedly emphasized that determining the explicit solutions of Hamiltonian equations is a task beyond the capabilities of mathematics. This situation justifies all attempts to obtain information about these solutions. For instance, a knowledge of the first integrals allows us to localize the dynamical trajectories in the phase space M 2n ...
openaire +1 more source
2018
Abstract This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the
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Abstract This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the
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Path Concepts in Hamilton-Jacobi Theory
American Journal of Physics, 1952It is pointed out that the classical analog to a wave function is not a single orbit but a set of paths as defined by the solution of the Hamilton-Jacobi equation. A review is given of Hamilton-Jacobi theory in language appropriate to these path concepts. It is shown that there is a classical analog to a wave packet.
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1990
The principal object of classical dynamics is to find where everything is at time t; that is, to find a set of q n (t). The principal object of quantum mechanics is to find a wave function ψ(q, t). From this you cannot calculate where everything is in the sense of classical physics, but you can calculate all there is to know. Lagrangian and Hamiltonian
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The principal object of classical dynamics is to find where everything is at time t; that is, to find a set of q n (t). The principal object of quantum mechanics is to find a wave function ψ(q, t). From this you cannot calculate where everything is in the sense of classical physics, but you can calculate all there is to know. Lagrangian and Hamiltonian
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Hamilton–Jacobi theory for gauge field theories
Journal of Geometry and Physics, 2020Manuel de León Rodríguez +1 more
exaly
Hamilton–Jacobi formalism on locally conformally symplectic manifolds
Journal of Mathematical Physics, 2021Cristina Sardon +2 more
exaly
The Hamilton–Jacobi Theory for Contact Hamiltonian Systems
Mathematics, 2021Manuel Lainz Valcázar +2 more
exaly