Körperbasis

Körperbasis is a term that can refer to several concepts, primarily within the fields of mathematics and physics. In mathematics, a Körperbasis, often translated as vector basis, is a set of linearly independent vectors that span a vector space. This means that any vector in the space can be uniquely expressed as a linear combination of the basis vectors. The number of vectors in a basis is called the dimension of the vector space. For example, in a two-dimensional Euclidean space, the standard basis consists of two vectors, often denoted as (1,0) and (0,1).

In physics, particularly in quantum mechanics, Körperbasis can refer to a basis of states for a quantum system. These states form a complete and orthonormal set, meaning that any possible state of the system can be represented as a linear combination of these basis states, and the basis states are mutually orthogonal and normalized. Common examples include the position basis and the momentum basis, or the spin up and spin down states for a spin-1/2 particle. The choice of basis can significantly simplify calculations and provide different perspectives on the system's behavior. The underlying mathematical structure is still that of a vector space, but the elements represent physical states.