The standard ampere is most accurately realized using a watt balance, but is in practice maintained via Ohm's Law from the units of electromotive force and resistance, the volt and the ohm, since the latter two can be tied to physical phenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect, respectively.

After the advent of quantum mechanics, work done by Landau in 1930 predicted the quantization of the Hall conductance for electrons confined in two dimensions.

Shortly after, in 1982, Störmer and Tsui observed the fractional quantum Hall effect where the conductivity was now a rational multiple of a constant.

In some contexts it is meaningful to speak of fractions of a charge ; for example in the charging of a capacitor, or in the fractional quantum Hall effect.

The quasiparticles of the fractional quantum Hall effect are also known as composite fermions, which are electrons with an even number of quantized vortices attached to them.

Experimental evidence for the existence of anyons exists in the fractional quantum Hall effect, a phenomenon observed in the two-dimensional electron gases that form the inversion layer of MOSFETs.

Coupled with the quantum Hall resistivity, this leads to a precise measurement of the Planck constant.

A quantum Hall state gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow.

A quantum spin Hall state is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat.

While the value of α can be estimated from the values of the constants appearing in any of its definitions, the theory of quantum electrodynamics ( QED ) provides a way to measure α directly using the quantum Hall effect or the anomalous magnetic moment of the electron.

The quantum Hall effect ( or integer quantum Hall effect ) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized values

The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively.

The effect of device and quantum noise, associated with such low input levels, will be described.

Further investigation and theoretical work showed that the effect was a radiationless effect more than an internal conversion effect by use of elementary quantum mechanics and transition rate and transition probability calculations.

The quantum hall effect is another example of measurements with high magnetic fields where topological properties such as Chern-Simons angle can be measured experimentally.

In quantum field theory, the Casimir effect and the Casimir – Polder force are physical forces arising from a quantized field.

In most materials diamagnetism is a weak effect, but in a superconductor a strong quantum effect repels the magnetic field entirely, apart from a thin layer at the surface.

Although modern quantum optics tells us that there also is a semi-classical explanation of the photoelectric effect — the emission of electrons from metallic surfaces subjected to electromagnetic radiation — the photon was historically ( although not strictly necessarily ) used to explain certain observations.

Heisenberg's principle was an attempt to provide a classical explanation of a quantum effect sometimes called non-locality.

Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment.

In a few materials, a much stronger interaction between spins arises because the change in the direction of the spin leads to a change in electrostatic repulsion between neighboring electrons, due to a particular quantum mechanical effect called the exchange interaction.

This is a direct effect of quantum mechanics: specifically, the zero point energy of the system is too high to allow freezing.

BCS theory views superconductivity as a macroscopic quantum mechanical effect.

:* Nanotechnology – rigorously, the study of materials where the effects of quantum confinement, the Gibbs – Thomson effect, or any other effect only present at the nanoscale is the defining property of the material ; but more commonly, it is the creation and study of materials whose defining structural properties are anywhere from less than a nanometer to one hundred nanometers in scale, such as molecularly engineered materials.

Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave – particle duality.

Since the complex algebra is responsible for the striking interference effect of quantum mechanics, phase of particles is therefore ultimately related to their quantum behavior.

It was possible to make estimates of the quantum yield by observing the extent of reduction of a uranyl oxalate actinometer solution illuminated for a known time in a typical reaction cell and making appropriate conversions based on the differences in the absorption spectra of uranyl oxalate and of chlorine, and considering the spectral distribution of the light source.

With the development of quantum mechanics, it was found that the orbiting electrons around a nucleus could not be fully described as particles, but needed to be explained by the wave-particle duality.

Explaining the behavior of these electron " orbits " was one of the driving forces behind the development of quantum mechanics.

Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step towards the understanding of electrons in atoms, and also a significant step towards the development of quantum mechanics in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms.

In the end, this was solved by the discovery of modern quantum mechanics and the Pauli Exclusion Principle.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital became known as an n-sphere in a three dimensional atom and was pictured as the mean energy of the probability cloud of the electron's wave packet which surrounded the atom.

However, this was the temperature of one particular degree of freedom a quantum property called nuclear spin not the overall average thermodynamic temperature for all possible degrees in freedom.

The analogy was completed when Hawking, in 1974, showed that quantum field theory predicts that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole.

Drude's classical model was augmented by Felix Bloch, Arnold Sommerfeld, and independently by Wolfgang Pauli, who used quantum mechanics to describe the motion of a quantum electron in a periodic lattice.

The first attempt at a microscopic description of magnetism was by Wilhelm Lenz and Ernst Ising through the Ising model that described magnetic materials as consisting of a periodic lattice of quantum spins that collectively acquired magnetization.

In 1995, a gas of rubidium atoms cooled down to a temperature of 170 nK was used to experimentally realize the Bose-Einstein condensate, a novel state of matter originally predicted by S. N. Bose and Albert Einstein, wherein a large number of atoms occupy a single quantum state.

The completeness of quantum mechanics ( thesis 1 ) was attacked by the Einstein-Podolsky-Rosen thought experiment which was intended to show that quantum physics could not be a complete theory.

In 1927, the first mathematically complete quantum description of a simple chemical bond, i. e. that produced by one electron in the hydrogen molecular ion, H < sub > 2 </ sub >< sup >+</ sup >, was derived by the Danish physicist Oyvind Burrau.

In 1929, the linear combination of atomic orbitals molecular orbital method ( LCAO ) approximation was introduced by Sir John Lennard-Jones, who also suggested methods to derive electronic structures of molecules of F < sub > 2 </ sub > ( fluorine ) and O < sub > 2 </ sub > ( oxygen ) molecules, from basic quantum principles.

The atoms in molecules model developed by Richard Bader was developed in order to effectively link the quantum mechanical picture of a molecule, as an electronic wavefunction, to chemically useful older models such as the theory of Lewis pairs and the valence bond model.

His work was a key aspect of Hermann Weyl and John von Neumann's work on the mathematical equivalence of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation and his namesake Hilbert space plays an important part in quantum theory.

", and he was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.

By the 1960s – 1970s quantum electrochemistry was developed by Revaz Dogonadze and his pupils.