﻿ Wave vector

# Wave vector

The wave vector in physics, a vector which is perpendicular to the wave front of a shaft. It has the unit 1 / m. In formulas, the sign is chosen for him usually. In most cases, it indicates the direction of propagation of the wave. When electromagnetic waves in certain media, however, the direction of the Poynting vector may differ for the flow of energy on the wave vector.

## Description

A plane wave propagating in the direction, can be in the form of

. Write

With the components in x -, y -and z- direction

Is the wave vector in the three -dimensional k-space, called reciprocal space in a particular direction.

The magnitude of the wave vector is the circular wavenumber, hence the name wave number vector. It is

The angular frequency, the phase velocity and wavelength.

## Wave vector and quantum numbers

The wave vector is not always quantized. It can have any positive value, the wavelength of light in vacuum.

The situation is different with particles in a finite space, for example in a potential well or an electron in a solid body. Here the allowed wave vectors are quantized, although they themselves do not represent the quantum numbers. The wave vector is rather a function of quantum numbers, or can its possible values ​​are counted by quantum numbers. This can be seen in analogy to the eigenenergies of a quantum- mechanical problem with a discrete spectrum: the index of the discrete energy is the quantum number, but not the energy itself

Viewpoint: For the solutions of the Schrödinger equation of a three-dimensional, infinitely high potential well of the edge lengths

With

The states of the particle, which is described as a shaft, so are the quantum numbers, and characterized. Instead of naming a state by this number triples, and the wave vector can be used. However, may not be referred to as the quantum number of or one of its components because of the wave vector is subject to the dimension a and the other is represented by real numbers.

For a potential well with particles to give vectors in k-space. So if this is fermions are electrons, there are two states that differ in the spin per wave vector.

## Wave vector and momentum

When photons ( Einstein equations ) and for matter waves ( de Broglie relation), the wave vector is a simple, proportional to the reduced Planck 's constant connection whose vectorial pulse to:

• Wave
• Quantum mechanics
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