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In quantum mechanics, resonance cross section occurs in the context of quantum scattering theory, which deals with studying the scattering of quantum particles from potentials. The scattering problem deals with the calculation of flux distribution of scattered particles/waves as a function of the potential, and of the state (characterized by ...
In such a scheme, the negative constitutive parameters are designed to appear around the Mie resonances of the inclusions: the negative effective permittivity is designed around the resonance of the Mie electric dipole scattering coefficient, whereas negative effective permeability is designed around the resonance of the Mie magnetic dipole ...
Pushing a person in a swing is a common example of resonance. The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate. A familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the ...
Resonance. Impedance; Reactance; Musical tuning; Orbital resonance; Tidal resonance; Oscillator. Harmonic oscillator; Electronic oscillator; Floquet theory; Fundamental frequency; Oscillation (Vibration) Fundamental matrix (linear differential equation) Laplace transform applied to differential equations; Sturm–Liouville theory; Wronskian ...
When , and are called the overlap and resonance (or exchange) integrals, respectively, while is called the Coulomb integral, and = simply expresses the fact that the are normalized. The n × n matrices [ S i j ] {\displaystyle [S_{ij}]} and [ H i j ] {\displaystyle [H_{ij}]} are known as the overlap and Hamiltonian matrices , respectively.
It is convenient to denote cavity frequencies with a complex number ~ = /, where = (~) is the angular resonant frequency and = (~) is the inverse of the mode lifetime. Cavity perturbation theory has been initially proposed by Bethe-Schwinger in optics [1], and Waldron in the radio frequency domain. [2]
In physical systems with resonance phenomena, Farey sequences provide a very elegant and efficient method to compute resonance locations in 1D [17] and 2D. [18] Farey sequences are prominent in studies of any-angle path planning on square-celled grids, for example in characterizing their computational complexity [19] or optimality. [20]
In quantum physics and quantum chemistry, an avoided crossing (AC, sometimes called intended crossing, [1] non-crossing or anticrossing) is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on continuous real parameters cannot become equal in value ("cross") except on a manifold of dimension . [2]