A report on Wave–particle duality

$Thomas Young's sketch of two-slit diffraction of waves, 1803$

The photoelectric effect. Incoming photons on the left strike a metal plate (bottom), and eject electrons, depicted as flying off to the right.

Propagation of de Broglie waves in 1d—real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the colour opacity) of finding the particle at a given point x is spread out like a waveform; there is no definite position of the particle. As the amplitude increases above zero the curvature decreases, so the amplitude decreases again, and vice versa—the result is an alternating amplitude: a wave. Top: Plane wave. Bottom: Wave packet.

Couder experiments, "materializing" the pilot wave model

Particle impacts make visible the interference pattern of waves.

A quantum particle is represented by a wave packet.

Interference of a quantum particle with itself.

Concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave.

- Wave–particle duality

$Thomas Young's sketch of two-slit diffraction of waves, 1803$

33 related topics with Alpha

Quantum mechanics

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Fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.

Position space probability density of a Gaussian wave packet moving in one dimension in free space.

1-dimensional potential energy box (or infinite potential well)

Some trajectories of a harmonic oscillator (i.e. a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wave function), with the real part shown in blue and the imaginary part shown in red. Some of the trajectories (such as C, D, E, and F) are standing waves (or "stationary states"). Each standing-wave frequency is proportional to a possible energy level of the oscillator. This "energy quantization" does not occur in classical physics, where the oscillator can have any energy.

Schematic of a Mach–Zehnder interferometer.

Max Planck is considered the father of the quantum theory.

The 1927 Solvay Conference in Brussels was the fifth world physics conference.

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave–particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).

Photon

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Elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.

Photoelectric effect: the emission of electrons from a metal plate caused by light quanta – photons.

The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency (rad⋅s−1) and the "space" axis represents the angular wavenumber (rad⋅m−1). Green and indigo represent left and right polarization

Thomas Young's double-slit experiment in 1801 showed that light can act as a wave, helping to invalidate early particle theories of light.

In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave model of electromagnetic radiation, leading to the idea that light-energy was packaged into quanta described by . Later experiments showed that these light-quanta also carry momentum and, thus, can be considered particles: The photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.

Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behaviour by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.

Photons in a Mach–Zehnder interferometer exhibit wave-like interference and particle-like detection at single-photon detectors.

Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.

Different electromagnetic modes (such as those depicted here) can be treated as independent simple harmonic oscillators. A photon corresponds to a unit of energy E = hν in its electromagnetic mode.

Like all elementary particles, photons are currently best explained by quantum mechanics, and exhibit wave–particle duality, their behavior featuring properties of both waves and particles.

Electron

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Subatomic particle whose electric charge is negative one elementary charge.

A beam of electrons deflected in a circle by a magnetic field

The Bohr model of the atom, showing states of an electron with energy quantized by the number n. An electron dropping to a lower orbit emits a photon equal to the energy difference between the orbits.

In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit. In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given quantum numbers, at that point.

Standard Model of elementary particles. The electron (symbol e) is on the left.

Example of an antisymmetric wave function for a quantum state of two identical fermions in a 1-dimensional box. If the particles swap position, the wave function inverts its sign.

A schematic depiction of virtual electron–positron pairs appearing at random near an electron (at lower left)

A particle with charge q (at left) is moving with velocity v through a magnetic field B that is oriented toward the viewer. For an electron, q is negative so it follows a curved trajectory toward the top.

Here, Bremsstrahlung is produced by an electron e deflected by the electric field of an atomic nucleus. The energy change E2 − E1 determines the frequency f of the emitted photon.

Probability densities for the first few hydrogen atom orbitals, seen in cross-section. The energy level of a bound electron determines the orbital it occupies, and the color reflects the probability of finding the electron at a given position.

A lightning discharge consists primarily of a flow of electrons. The electric potential needed for lightning can be generated by a triboelectric effect.

Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity as v approaches c.

Pair production of an electron and positron, caused by the close approach of a photon with an atomic nucleus. The lightning symbol represents an exchange of a virtual photon, thus an electric force acts. The angle between the particles is very small.

An extended air shower generated by an energetic cosmic ray striking the Earth's atmosphere

Aurorae are mostly caused by energetic electrons precipitating into the atmosphere.

During a NASA wind tunnel test, a model of the Space Shuttle is targeted by a beam of electrons, simulating the effect of ionizing gases during re-entry.

Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light.

Niels Bohr

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Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922.

Bohr and Margrethe Nørlund on their engagement in 1910.

The Bohr model of the hydrogen atom. A negatively charged electron, confined to an atomic orbital, orbits a small, positively charged nucleus; a quantum jump between orbits is accompanied by an emitted or absorbed amount of electromagnetic radiation.

The evolution of atomic models in the 20th century: Thomson, Rutherford, Bohr, Heisenberg/Schrödinger

The Niels Bohr Institute, part of the University of Copenhagen

Bohr and Albert Einstein (image from 1925) had a long-running debate about the metaphysical implication of quantum physics.

Werner Heisenberg (left) with Bohr at the Copenhagen Conference in 1934

Bohr with James Franck, Albert Einstein and Isidor Isaac Rabi (LR)

Bohr's coat of arms, 1947. Argent, a taijitu (yin-yang symbol) Gules and Sable. Motto: Contraria sunt complementa ("opposites are complementary").

The Theory of Spectra and Atomic Constitution (Drei Aufsätze über Spektren und Atombau), 1922

He conceived the principle of complementarity: that items could be separately analysed in terms of contradictory properties, like behaving as a wave or a stream of particles.

Louis de Broglie

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French physicist and aristocrat who made groundbreaking contributions to quantum theory.

François-Marie, 1st duc de Broglie (1671–1745) ancestor of Louis de Broglie and Marshal of France under Louis XIV of France

This concept is known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central part of the theory of quantum mechanics.

Erwin Schrödinger

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Nobel Prize-winning Austrian-Irish physicist who developed a number of fundamental results in quantum theory: the Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time.

Bust of Schrödinger, in the courtyard arcade of the main building, University of Vienna, Austria

Schrödinger (front row 2nd from right) and De Valera (front row 4th from left) at Dublin Institute for Advanced Studies in 1942

Annemarie and Erwin Schrödinger's gravesite; above the name plate Schrödinger's quantum mechanical wave equation is inscribed:

During this period Schrödinger turned from mainstream quantum mechanics' definition of wave–particle duality and promoted the wave idea alone, causing much controversy.

$Same double-slit assembly (0.7 mm between slits); in top image, one slit is closed. In the single-slit image, a diffraction pattern (the faint spots on either side of the main band) forms due to the nonzero width of the slit. This diffraction pattern is also seen in the double-slit image, but with many smaller interference fringes.$

Double-slit experiment

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Demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena.

Buildup of interference pattern from individual particle detections

A diagram of Wheeler's delayed choice experiment, showing the principle of determining the path of the photon after it passes through the slit

A laboratory double-slit assembly; distance between top posts approximately 2.5 cm (one inch).

Near-field intensity distribution patterns for plasmonic slits with equal widths (A) and non-equal widths (B).

$Two-slit diffraction pattern by a plane wave$

Photo of the double-slit interference of sunlight.

Two slits are illuminated by a plane wave.

One of an infinite number of equally likely paths used in the Feynman path integral (see also: Wiener process)

An example of the uncertainty principle related to the relational interpretation. The more that is known about the position of a particle, the less is known about the velocity, and vice versa

Thomas Young's experiment with light was part of classical physics long before the development of quantum mechanics and the concept of wave–particle duality.

Atom

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Smallest unit of ordinary matter that forms a chemical element.

The Geiger–Marsden experiment:
Left: Expected results: alpha particles passing through the plum pudding model of the atom with negligible deflection.
Right: Observed results: a small portion of the particles were deflected by the concentrated positive charge of the nucleus.

The Bohr model of the atom, with an electron making instantaneous "quantum leaps" from one orbit to another with gain or loss of energy. This model of electrons in orbits is obsolete.

The binding energy needed for a nucleon to escape the nucleus, for various isotopes

A potential well, showing, according to classical mechanics, the minimum energy V(x) needed to reach each position x. Classically, a particle with energy E is constrained to a range of positions between x1 and x2.

3D views of some hydrogen-like atomic orbitals showing probability density and phase (g orbitals and higher are not shown)

This diagram shows the half-life (T½) of various isotopes with Z protons and N neutrons.

These electron's energy levels (not to scale) are sufficient for ground states of atoms up to cadmium (5s2 4d10) inclusively. Do not forget that even the top of the diagram is lower than an unbound electron state.

An example of absorption lines in a spectrum

Graphic illustrating the formation of a Bose–Einstein condensate

Scanning tunneling microscope image showing the individual atoms making up this gold (100) surface. The surface atoms deviate from the bulk crystal structure and arrange in columns several atoms wide with pits between them (See surface reconstruction).

Periodic table showing the origin of each element. Elements from carbon up to sulfur may be made in small stars by the alpha process. Elements beyond iron are made in large stars with slow neutron capture (s-process). Elements heavier than iron may be made in neutron star mergers or supernovae after the r-process.

Electrons, like other particles, have properties of both a particle and a wave.

Light

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Electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.

The electromagnetic spectrum, with the visible portion highlighted

Beam of sun light inside the cavity of Rocca ill'Abissu at Fondachelli-Fantina, Sicily

$Due to refraction, the straw dipped in water appears bent and the ruler scale compressed when viewed from a shallow angle.$

Hong Kong illuminated by colourful artificial lighting.

$Thomas Young's sketch of a double-slit experiment showing diffraction. Young's experiments supported the theory that light consists of waves.$

Like all types of electromagnetic radiation, visible light propagates by massless elementary particles called photons that represents the quanta of electromagnetic field, and can be analyzed as both waves and particles.

Magnetic field lines visualized using iron filings. When a piece of paper is sprinkled with iron filings and placed above a bar magnet, the filings align according to the direction of the magnetic field, forming arcs.

Quantum field theory

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Theoretical framework that combines classical field theory, special relativity, and quantum mechanics.

Elementary particles of the Standard Model: six types of quarks, six types of leptons, four types of gauge bosons that carry fundamental interactions, as well as the Higgs boson, which endow elementary particles with mass.

In 1924, Louis de Broglie proposed the hypothesis of wave–particle duality, that microscopic particles exhibit both wave-like and particle-like properties under different circumstances.