Matter wave

The model of matter waves states that each particle a wave of a particular wavelength can be assigned. It is used to describe quantum effects of matter as scattering behavior and interference that can not be explained by the particle model of classical mechanics; compare wave -particle duality.

History

After the discovery of the quantization of light by Albert Einstein in the study of the photoelectric effect the dilemma of whether light is to be described as a wave or as a particle originated. Louis -Victor de Broglie reasoned that when photons show the particle and wave character, then classical particles would have such a dual behavior. In 1924, he postulated in his doctoral thesis, the matter waves, and thus arose the wave -particle duality to the general principle.

1927 Clinton Davisson and Lester Germer succeeded in the Davisson -Germer experiment to prove the wave properties of electrons through interference experiments over a nickel single crystal. De Broglie wavelength formula was confirmed that, just like in the aftermath of similar interference experiments with other elementary particles, atoms, and even molecules. For his theory of Louis de Broglie was awarded the 1929 Nobel Prize in Physics. Most impressive is the double slit experiment with electrons, the Claus Jönsson 1959 realized at the University of Tübingen.

In quantum mechanics, it is assumed that a quant no defined location can be assigned, but only a probability, which is described by a probability wave. This probability wave has a wave equation follow (eg Schrödinger or Dirac equation). Properties that one associates classical particles are explained by highly localized wave packets.

See also: Born's probability interpretation.

The de Broglie wavelength

According to de Broglie each particle can be assigned a wave, which is characterized by the wavelength. As an example, the photon is considered, which can be interpreted in Maxwell's theory of electromagnetism as a wave packet.

A photon has no rest mass, but energy:

It is

• The reduced Planck constant
• The angular frequency and
• The wave frequency.

Although it has no rest mass, the photon also has a pulse:

With the wave vector of the matter wave.

Because of the definition of the reduced Planck's constant, this results in:

With the angular wave number and thus

Louis de Broglie generalized this equation to arbitrary particles ( De Broglie equation):

Where here is the relativistic momentum of a particle with rest mass and velocity:

(: Speed ​​of light).

The wavelength, and therefore the size of the observed effects therefore depends on the mass and the velocity of the particle. Therefore, matter waves are easy to observe only at very light particles (eg electrons). Through interference experiments in the research group around Markus Arndt at the University of Vienna, the validity of the theory of matter waves, however, was demonstrated for large complex molecules of several hundred atoms with several thousand proton masses.