Relation of dispersion

In Theoretical physics, a relation of dispersion is a relation between the Pulsation $\backslash \; omega$ and the Vecteur of wave $\backslash \; vec\; \{K\}$ of a monochromatic Onde.

By extension, the Dualité wave-corpuscle of the Quantum physics leads to the introduction of relation of dispersion for a particle, like relation between its energy $E$ and its Quantité of movement $\backslash \; vec\; \{p\}$.

Examples

Monochromatic wave of celerity C in a nondispersive medium

A nondispersive medium is characterized by an index N independent of the pulsation. While noting: $K\; =\; ||\; \backslash \; vec\; \{K\}\; ||$, the relation of dispersion is written:

The Speed of phase is then constant :

and is equal to the Speed of group:

Monochromatic wave of celerity C in a dispersive medium

In a dispersive medium, the index N depends on the pulsation. While noting: $K\; =\; ||\; \backslash \; vec\; \{K\}\; ||$, the relation of dispersion is written:

The Speed of phase depends then explicitly on the pulsation:

The Speed of group is not in general equal any more at the speed of phase, but is connected to him by the relation of Rayleigh:

Nonrelativistic particle of mass m

While noting: $p\; =\; ||\; \backslash \; vec\; \{p\}\; ||$, the relation of dispersion is written:

Relativistic particle of mass m

Relativistic particle of null mass

Related articles

• Electrodynamic of the continuous mediums

• Quantum theory of the fields

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