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Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either ρ ( r ) {\displaystyle \rho ({\textbf {r}})} or n ( r ) {\displaystyle n ...
Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
The two colors show the phase or sign of the wave function in each region. Each picture is domain coloring of a ψ(x, y, z) function which depends on the coordinates of one electron. To see the elongated shape of ψ(x, y, z) 2 functions that show probability density more directly, see pictures of d-orbitals below.
The theory is based on the calculus of variations of a thermodynamic functional, which is a function of the spatially dependent density function of particles, thus the name. The same name is used for quantum DFT, which is the theory to calculate the electronic structure of electrons based on spatially dependent electron density with quantum and ...
The Fukui function is named after Kenichi Fukui, who investigated the frontier orbitals described by the function, specifically the HOMO and LUMO. [3] Fukui functions are related in part to the frontier molecular orbital theory (also known as the Fukui theory of reactivity and selection, also developed by Kenichi Fukui) which discusses how nucleophiles attack the HOMO while at the same time ...
The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.
where D is the diffusion coefficient for the electron in the considered medium, n is the number of electrons per unit volume (i.e. number density), q is the magnitude of charge of an electron, μ is electron mobility in the medium, and E = −dΦ/dx (Φ potential difference) is the electric field as the potential gradient of the electric potential.
where ρ is the density of the material, Z its atomic number, A its relative atomic mass, N A the Avogadro number and M u the Molar mass constant. In the figure to the right, the small circles are experimental results obtained from measurements of various authors, while the red curve is Bethe's formula. [ 4 ]