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Electron quantization in arbitrarily shaped gold islands on MgO thin films
Related concepts (35)
Molecular orbital diagram
A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals.
Quantum Hall effect
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,.
Artificial island
An artificial island is one that has been constructed by humans rather than formed through natural processes. Other definitions may suggest that artificial islands are lands with the characteristics of human intervention in their format process, while others argue that artificial islands are created by expanding existing islets, constructing on existing reefs, or amalgamating several islets together. Although constructing artificial islands is not a modern phenomenon, there is no definite legal definition of it.
Particle in a ring
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle ) is Using polar coordinates on the 1-dimensional ring of radius R, the wave function depends only on the angular coordinate, and so Requiring that the wave function be periodic in with a period (from the demand that the wave functions be single-valued functions on the circle), and that they be normalized leads to the conditions and Under these conditions, the solution to the Schrödinger equation is given by The energy eigenvalues are quantized because of the periodic boundary conditions, and they are required to satisfy or The eigenfunction and eigenenergies are where Therefore, there are two degenerate quantum states for every value of (corresponding to ).
Island
An island or isle is a piece of subcontinental land completely surrounded by water. Very small islands such as emergent land features on atolls can be called islets, skerries, cays or keys. An island in a river or a lake island may be called an eyot or ait, and a small island off the coast may be called a holm. Sedimentary islands in the Ganges Delta are called chars. A grouping of geographically or geologically related islands, such as the Philippines, is referred to as an archipelago.