Wave–particle duality

The wave -particle duality is a principle of quantum physics, according to which the objects of quantum physics alike the properties of classical waves like that must be attributed by classical particles.

• Classical waves propagate in space. They weaken or strengthen by superposition and can act simultaneously at different locations with different strength.
• A classical particle can be present at a time only at a specific location. Only there it works, but always with its total energy, charge, momentum, etc.

Both properties seem to contradict each other. Nevertheless, it was shown in several key experiments for different quantum objects that both properties are present. It is therefore impossible to develop a clear and classically based perspectives notion that is the wave -particle duality justice. The question of whether, for example, electrons or photons "real" particles or waves in the sense of the usual view is had, therefore, no need to answer. It is, rather, a separate class of quantum objects, either leave depending on the type of measurement that is performed in them their wave or only its particle property appear, but not both at the same time. The quantum mechanics solved the problem after the Copenhagen interpretation (1927 ) and the complementarity principle formulated there initially to the effect that each observed property was not attributable solely to the quantum object, but performing a quantum phenomenon of the entire assembly of quantum object and measuring apparatus. Later a number of other interpretations of quantum mechanics originated with alternative approaches to explanation.

The quantum field theory understands particles and interactions as excitations of fields. Thus there is no fundamental difference between these two categories. The contrasts that make up the wave -particle duality, omitted.

• 5.1 Compton effect
• 5.2 Electron diffraction at the crystal lattice
• 5.3 Interference of larger molecules

• 6.1 Quantum mechanics and statistical physics
• 6.2 Macroscopic observation

Historical beginnings

The history of the discovery of the wave -particle duality in electromagnetic radiation dates back to the 17th century, when the laws of geometrical optics for reflection and refraction of light rays have been studied in detail. There are two competing theories emerged:

• Christiaan Huygens (1629-1695) was the optical laws suggest using the wave theory and is therefore regarded as the founder of wave optics. Developed by him Huygens' principle is applied still unchanged today.
• Isaac Newton (1643-1727) suggested the same laws by using the Korpuskelvorstellung, after which the light is a stream of light particles faster.

Both theories were consistent with the former observations agree equally well, although their starting points appeared incompatible. In the absence of experimental possibilities of distinction sat down, mainly due to the greater authority of Newton's corpuscular theory by the first. But in 1802 Thomas Young showed the wave character of light after. Young demonstrated with the double slit experiment that light can cancel out by interference, which is unthinkable for particle beams. The wave nature of light has been widely recognized only late in the 19th century, after further discoveries were made that did not fit to the corpuscular theory: polarization (François Arago and others), diffraction ( Augustin Jean Fresnel theoretical prediction by, inter alia, experimental evidence of Poisson spot by Arago in 1821 ), lower velocity of propagation in optically dense media (Jean Foucault 1853), the relationship between the speed of light and electrodynamics ( James C. Maxwell 1867) and the electromagnetic waves ( Heinrich Hertz 1886).

1900 saw Max Planck in the analysis of the thermodynamic equilibrium between the electromagnetic waves of thermal radiation and the surrounding walls, that the transfer of energy between radiation and matter can take place only in quanta of size ( Planck's constant, frequency of the wave ). 1905 Albert Einstein had claimed that even the photoelectric effect, the energy transfer can not be explained to the electrons with light waves, but with light quanta with the energy given by Planck. Finally, Einstein showed in 1909 that the heat radiation must show statistical fluctuations whose size can only be interpreted that the radiation itself consists of waves and quanta. He called for the development of a theory in which the radiation has both particle nature and wave nature, and thus is considered as the author of the principle of wave -particle duality. The solution, he suggested, however, mistakenly in the sense that the ever -varying electromagnetic wave would result from the superposition of the fields of many closely spaced " singular points ".

Einstein and the photons ( light quanta)

In 1905, Albert Einstein postulated to explain the photoelectric effect, in turn, that the light from light quanta ( photons) there. He was referring to works of the Planck blackbody radiator from 1900 in which it first took a quantization of energy levels of the harmonic oscillator. This was first done purely from mathematical considerations. The photon is a single, so " discrete " portion of energy E dar. light can absorb or emit energy only in integral multiples of that amount. The energy of a photon resulting from Planck's studies of

Where the Planck constant, the frequency, the speed of light and the wavelength of the photon are.

This relationship also applies to mechanical waves, such as for lattice vibrations in a solid body. The quanta are called phonons in this case.

De Broglie and the wave nature of particles

Louis de Broglie postulated in 1924 that even mass -prone particles have a wave character. He was for a particle with momentum p has a wavelength of

Of.

With the help of de Broglie's formula a diffraction behavior of particles can be predicted, which was experimentally confirmed in 1927 by diffraction of an electron beam on a nickel crystal by Davisson and Germer, and finally by the electron double-slit experiment of Claus Jönsson in 1961. The wave nature of matter is now detected even for much larger particles, for example, complex molecules such as fullerenes.

The average de Broglie wavelength of particles at a given temperature is referred to as thermal wavelength.

The double slit experiment

Particularly impressive shows the behavior of quantum objects in the so-called double -slit experiment. Thomas Young was the first to demonstrate the wave nature of light with this experiment. The going back to Newton corpuscular theory seemed so at first refuted.

Experimental setup

Going from a source "rays" - it can be either electromagnetic waves or particles of matter - and meet a panel with two very fine, closely spaced slits. This diaphragm is called the " double slit ". Behind the shield is a shield. The rays passing through the double slit, apply to the screen and be registered there in a suitable manner.

Classical waves

If it is in the beam to classical waves, as they show a typical diffraction pattern, as can be seen in the adjacent figure 1: Depending on the wavelength of the radiation and the geometry of the double gap appearing areas on the screen strip-like light or dark. The bright spots are located exactly where the two emanating from the double slit elementary waves have a path difference is an integer multiple of the wavelength. Just then the two waves are in fact "in phase" and interfere constructively. Between these points the two waves are in antiphase and cancel each other by destructive interference from.

The diffraction pattern continuously Apart from its strip-like structure appears. The brightness in one place can take on any value between total darkness and maximum illumination.

Classical particles

Classical particles (ie single mass points) do not interfere (see Figure 2). You get either the left or right gap and then shall each within a clearly defined area on the screen. Consequently, appear on the screen exactly two light stripes (one for one of the column). A closer look at the grain structure of the two strips falls on. Each particle strikes at a single point and leaves behind a bright spot. There is no continuous brightness profile. A place is labeled, either light or dark, either because he was hit by a particle or not.

Quantum objects

The objects of quantum physics, however, behave as it illustrates the third figure: As with the classical waves shows the intensity distribution on the screen a typical diffraction pattern. So there must be interference occur. On the other hand the intensity curve is not continuous. There bright spots appear, but in different density. Each quantum object may (at least later ) are assigned a particular location at which it is hit on the screen. Therefore, it is clearly a countable, point-like object.

Discussion

Thus, the quantum objects show obvious characteristics of both classical models: they interfere with each other, which is typical for waves. On the other hand, they are countable and point- what the wave nature contradicts entirely and rather points to a particle nature. It is not possible without contradiction to modify one of the two models so that it could explain all aspects of the experimental result. For example, a particle can only go through one of two slits, but not through both. If you alternately covering one of the two column, one obtains the distribution of particles that have gone through either the right or the left gap. This corresponds approximately to the distribution in Figure 2, when one sees beyond the diffraction at the edges, which always occur in quantum objects. If you open again both slits, the diffraction pattern of Figure 3 appears It follows that one can not explain the distribution pattern of quantum objects on the screen, if it is assumed that the single quantum object either way by the one or by the other gap takes. Still, there must be individual, indivisible, point-like particles, because as such they are on the screen spatially and temporally separated from each registered. The notion of a spatially extended wave going through both column and can then interfere with itself, is therefore equally wrong.

So quantum objects show a behavior that can be explained satisfactorily neither with the classical wave picture nor with the classical particle picture.

Historic Key experiments

Since the wave -particle duality was discovered rather indirectly through the investigations of the spectrum of thermal radiation ( Planck ), the photoelectric effect and the statistical variation of the thermal radiation (Einstein), to the possibility of matter wave ( de Broglie ), in wave mechanics ( Schrödinger ) but plays a central role, it was the aim of further experiments to examine the wave -particle duality in a much more direct way.

Compton effect

Arthur Compton in 1923 could prove in the scattering of electromagnetic waves that they just behave like individual particles that own and run an elastic collision with an electron, the energy and momentum of a photon. In electromagnetic waves it was X-rays, whose wave character has been exploited in the same experiment to to determine by Bragg diffraction by a crystal, ie, an interference phenomenon, the energy before and after the impact of each photon. In addition, the struck electron and photon a departing were also each other simultaneously detected, so that other explanations than were refuted with single, independent shocks.

Electron diffraction at the crystal lattice

Clinton Davisson and Lester Germer in 1927 were able to show that a beam of electrons is partially reflected back without loss of energy of a crystal surface, then interference phenomena shows such as X-rays at the Bragg diffraction. This can be described physically only with the spread of each electron in the form of a wave. The electrons are on the other hand, particles, in the same experiment it is clear that another part of the incident electrons was zusammgestoßen elastically respectively with an electron energy of the crystal, and thereby lost. The so- scattered electrons do not form an interference pattern.

Interference of larger molecules

In order to clarify whether the wave -particle duality belongs only to elementary particles such as photons and electrons or composite systems, atoms and molecules have been studied. Corresponding interference patterns were first demonstrated in 1930 by Immanuel Estermann and Otto Stern with H2 molecules after reflection from a crystal surface of LiF. They corresponded exactly to the predicted for the molecules of matter waves. Towards particles with increasing mass succeeded Olaf Nairz, Markus Arndt, and Anton Zeilinger in 1999 to produce interference pattern at C60. This also said molecules " buckyballs " consist of 60 carbon atoms, which are composed in the form of a football and contains a total of 360 protons, 360 neutrons and 360 electrons. They are about 4 nm in size and can be seen under a scanning tunneling microscope already well as a small " clumps ". Your de Broglie wavelength was about 3 pm and was four to five orders of magnitude smaller than the lattice constant of 100 nm - currently the smallest technically feasible. The interference maxima of the screen in about 1 m, therefore, had a pitch of 0.03 mm. In the diffraction experiment, the particle nature of buckyballs was also made clear that they were counted individually after passing through the diffraction grating using a particle detector.

Resolution of the wave -particle duality in quantum mechanics

Each particle is described in quantum mechanics by a wave function. The wave function of a particle is complex and thus not a measure. Only their absolute square can be used as probability (more precisely, as the volume density of probability) are interpreted the particle and determines the experiment. The time development of the wave function of the particle, and thus the change in its probability is described by the Schrödinger equation.

Quantum mechanics and statistical physics

In the microscopic region of the wave -particle duality serves as a heuristic explanation of some physical phenomena. So hangs after de Broglie wavelength of a particle on its velocity and thus also on its temperature. At low temperatures, the de Broglie wavelength can be larger than the atoms of atomic diameter and overlap, making the effects of superfluidity of helium -3 and helium -4 can be explained in part. For a complete and quantitative treatment of these topics, however, quantum mechanics must be used.

Macroscopic observation

The wave nature of the particles does not show up in macroscopic objects, which has two main causes:

• Even at slow motion have macroscopic objects due to their large mass, a wavelength that is significantly smaller than the dimensions of the object. In this case, one can no longer treat the entire object as a quantum mechanical object, but must describe its components separately.
• In macroscopic objects permanently expire thermodynamically irreversible processes and there are photons ( thermal radiation) exchanged with the environment. Both lead to the decoherence of the system, which means that one may initially be interference -able condition very quickly not capable of interference converts to a, then as a classical particle, so do not behave like a wave.

Example of X-ray spectroscopy

In the X-ray spectroscopy to make the properties of the characteristic X-rays advantage. The X-ray spectrum of a substance gives information about the internal structure of its atoms and can therefore be used for the analysis. The measurement can be done either wavelength or energy dispersive. In the energy-dispersive methods are directly the energies of the individual photons is determined ( ie, in the classical manner of speaking a " particle property " ), from which can be calculated the atomic energy levels. For the same purpose but you can also the wavelength of X- rays to measure (ie, a " wave property "). Both - energy and wavelength - are characteristic features of X-ray quanta that are neither classical waves can be classical particles thus still.