In mathematics, an ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence of n scalars called coordinates. If two different bases are considered, the coordinate vector that represents a vector v on one basis is, in general, different from the coordinate vector that represents v on the other basis. A change of basis consists of converting every assertion expressed in terms of coordinates relative to one basis into an assertion expressed in terms of coordinates relative to the other basis.
Such...
Die Symmetrische Orthogonalisierung ist ein von Per-Olov Löwdin (1916–2000) entwickeltes, in der Quantenchemie häufig eingesetztes Orthogonalisierungsverfahren. Als solches dient es dazu, aus einem gegebenen nichtorthogonalen Satz von Vektoren einen orthogonalen Satz zu erzeugen, bei dem für je zwei verschiedene Vektoren das Skalarprodukt gleich Null ist.
== Beschreibung ==
Gegeben sei eine Basis
S
{\displaystyle S}
für einen Untervektorraum
V
{\displaystyle V}
eines reellen oder komplexen endlichdimensionalen…
The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space H. It is named after V. A. Fock who first introduced it in his 1932 paper "Konfigurationsraum und zweite Quantelung" ("Configuration space and second quantization").
Informally, a Fock space is the sum of a set of Hilbert spaces representing zero particle states, one particle states, two particle states, and so on. If the identical particles are bosons, the n-particle states are vectors in a symmetrized...
