Position Space

Position space (also real space or coordinate space) is the set of all position vectors r of an object in space (usually 3D). The position vector defines a point in space. If the position vector varies with time it will trace out a path or surface, such as the trajectory of a particle.

Momentum space or k-space is the set of all wavevectors k, associated with particles - free and bound. The terms "momentum" (symbol p, also a vector) and "wavevector" are used interchangeably due to the De Broglie relation p = ħk, meaning they are equivalent up to proportionality, although this is not true in a crystal, see below.

This is an example of Pontryagin duality.

The position vector r has dimensions of length, the k-vector has dimensions of reciprocal length, so k is the frequency analogue of r, just as angular frequency ω is the inverse quantity and frequency analogue of time t. Physical phenomena can be described using either the positions of particles, or their momenta, both formulations equivalently provide the same information about the system in consideration. Usually r is more intuitive and simpler than k, though the converse is also true, such as in solid-state physics.

Other articles related to "position, position space, space":

Position (vector) - Applications - Linear Algebra
... Linear algebra allows for the abstraction of an n-dimensional position vector ... A position vector can be expressed as a linear combination of basis vectors The set of all position vectors form position space (a vector space whose elements are the ... The notion of "space" is intuitive since each xi (i = 1,2.. ...
Relativistic Propagators - Position Space - Feynman Propagator
... A contour going under the left pole and over the right pole gives the Feynman propagator ... This choice of contour is equivalent to calculating the limit (see Huang p30) Here Here and are two points in Minkowski spacetime, and the dot in the exponent is a four-vector inner product ...