**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** = *ħ***k**, 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.

Read more about Position Space: Position and Momentum Spaces in Quantum Mechanics, Relation Between Space and Reciprocal Space, Unitary Equivalence Between Position and Momentum Operator, Reciprocal Space and Crystals, See Also

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

... 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.. ...

**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 ...

**Position Space**- See Also

... Phase space Reciprocal space Configuration space. ...

### Famous quotes containing the words space and/or position:

“To play is nothing but the imitative substitution of a pleasurable, superfluous and voluntary action for a serious, necessary, imperative and difficult one. At the cradle of play as well as of artistic activity there stood leisure, tedium entailed by increased spiritual mobility, a horror vacui, the need of letting forms no longer imprisoned move freely, of filling empty time with sequences of notes, empty *space* with sequences of form.”

—Max J. Friedländer (1867–1958)

“Feminism, like Boston, is a state of mind. It is the state of mind of women who realize that their whole *position* in the social order is antiquated, as a woman cooking over an open fire with heavy iron pots would know that her entire housekeeping was out of date.”

—Rheta Childe Dorr (1866–1948)