Position and Momentum Space

Position And Momentum Space

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.