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.

The quantum Hall effect was discovered by Klaus von Klitzing in 1980 when he observed the Hall conductivity to be integer multiples of a fundamental constant.

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 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.

These estimates indicated that the quantum yield for the exchange of chlorine with liquid carbon tetrachloride at 65-degrees is of the order of magnitude of unity.

Each orbital is defined by a different set of quantum numbers ( n, l, and m ), and contains a maximum of two electrons each with their own spin quantum number.

Specifically, in quantum mechanics, the state of an atom, i. e. an eigenstate of the atomic Hamiltonian, is approximated by an expansion ( see configuration interaction expansion and basis set ) into linear combinations of anti-symmetrized products ( Slater determinants ) of one-electron functions.

In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space.

In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy.

In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy.

where X is the energy level corresponding to the principal quantum number n, type is a lower-case letter denoting the shape or subshell of the orbital and it corresponds to the angular quantum number l, and y is the number of electrons in that orbital.

In X-ray notation, the principal quantum number is given a letter associated with it.

A given ( hydrogen-like ) atomic orbital is identified by unique values of three quantum numbers: n, l, and m < sub > l </ sub >.

The principal quantum number, n, describes the energy of the electron and is always a positive integer.

The azimuthal quantum number,, describes the orbital angular momentum of each electron and is a non-negative integer.

The magnetic quantum number,, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer.

Alpha decay, like other cluster decays, is fundamentally a quantum tunneling process.

Classically, it is forbidden to escape, but according to the ( then ) newly-discovered principles of quantum mechanics, it has a tiny ( but non-zero ) probability of " tunneling " through the barrier and appearing on the other side to escape the nucleus.

In particle physics, antimatter is material composed of antiparticles, which have the same mass as particles of ordinary matter but have opposite charge and quantum spin.

A unified interpretation of antiparticles is now available in quantum field theory, which solves both these problems.

This is an example of renormalization in quantum field theory — the field theory being necessary because the number of particles changes from one to two and back again.