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The general results presented above for Hamilton's principle can be applied to optics using the Lagrangian defined in Fermat's principle.The Euler-Lagrange equations with parameter σ =x 3 and N=2 applied to Fermat's principle result in ˙ = with k = 1, 2 and where L is the optical Lagrangian and ˙ = /.
Hamilton's optico-mechanical analogy is a conceptual parallel between trajectories in classical mechanics and wavefronts in optics, introduced by William Rowan Hamilton around 1831. [1] It may be viewed as linking Huygens' principle of optics with Maupertuis' principle of mechanics.
The Dicke model is a fundamental model of quantum optics, ... the Hamiltonian in ... effects of additional terms in the Hamiltonian of Eq. 1. [6] For example, ...
Analytical mechanics, or reformulations of Newton's laws of motion, most notably Lagrangian and Hamiltonian mechanics; Geometric optics, especially Lagrangian and Hamiltonian optics; Variational method (quantum mechanics), one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states;
For example, in geometrical optics, light can be considered either as “rays” or waves. The wave front can be defined as the surface that the light emitted at time = has reached at time . Light rays and wave fronts are dual: if one is known, the other can be deduced.
The Malus-Dupin theorem is a theorem in geometrical optics discovered by Étienne-Louis Malus in 1808 [1] and clarified by Charles Dupin in 1822. [2] Hamilton proved it as a simple application of his Hamiltonian optics method. [3] [4] Consider a pencil of light rays in a homogenous medium that is perpendicular to some surface.
The losses in photonic systems, are a feature used to study non-Hermitian physics. [2] Adding non-Hermiticity (such as dichroism) to photonic systems which present Dirac points transforms these degeneracy points into pairs of exceptional points.
The Hamiltonian of the particle is: ^ = ^ + ^ = ^ + ^, where m is the particle's mass, k is the force constant, = / is the angular frequency of the oscillator, ^ is the position operator (given by x in the coordinate basis), and ^ is the momentum operator (given by ^ = / in the coordinate basis).