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In physics and geometry, there are two intertwined vector spaces. 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 is the set of all momentum vectors p of an object in space (again usually 3D). The momentum vector corresponds to the motion of the object. The idea transcends all of physics, classical and quantum mechanics. However, in quantum mechanics, the De Broglie relation p = ''ħ''k states that momentum and wavevectors for a free particle are proportional to each other. The set of all wavevectors k forms k-space. and when it is unambiguous, the terms "momentum" (symbol p, also a vector) and "wavevector" are used interchangeably. The De Broglie relation is not true in a crystal. The duality between position and momentum is an example of ''Pontryagin duality''. The position vector r has dimensions of length, the momentum vector has units of ()()()−1, and 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. ==Position and momentum spaces in classical mechanics== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「position and momentum space」の詳細全文を読む スポンサード リンク
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