Local space

As a spatial domain in which is physics of the space designated for the description of the spatial degree of freedom of a physical system (e.g., as a particles , more particles field , the body , the crystal lattice ) is used.

In the case of a single particle or a field, spatial space is ordinary three-dimensional Euclidean space , which corresponds to the space that we humans experience with our senses and in which we move. In the case of several particles, a body or a crystal lattice, these can also be higher-dimensional Euclidean spaces.

Subspace of the phase space

In addition to their spatial degrees of freedom, many physical systems also have other degrees of freedom (such as speed , momentum or spin ), which are described in additional spaces, e.g. B. the momentum in momentum space . So an electron has a spatial and a spin degree of freedom, its description only in spatial space is therefore incomplete.

In mechanics and statistical physics , the state of a system is completely determined by a point in phase space . This is the Cartesian product of space and momentum space. Quantum mechanical states (like the electron in the atom above) are generally described in product spaces from Hilbert spaces .

Frequency space as an alternative

Some physical systems can be described equally in different rooms. The approach is only related to the problem, so the technical processing of certain questions in one of the two rooms is often easier:

• Vibrations or waves can be described either in the spatial or in the (spatial) frequency domain due to the Fourier transformation .
• In electrodynamics and quantum mechanics , the space of the Fourier-transformed probability waves is called the momentum space . Thus in quantum mechanics there is the position representation as well as the momentum representation .
• Locally periodic structures (crystal lattices) are described in crystallography or solid-state physics either in spatial or in reciprocal space (space of spatial frequencies ).

See also

• Configuration space

Individual evidence

1. ^ Dieter Meschede: Gerthsen Physics . Springer, August 19, 2003, ISBN 978-3-540-02622-8 , p. 247-.
2. ↑ Siegmund Brandt, HD Dahmen: Mechanics: An introduction to experiment and theory . Springer, September 15, 2004, ISBN 978-3-540-21666-7 , pp. 67–.
3. ↑ Florian Scheck: Theoretical Physics 3: Classical Field Theory. From electrodynamics to gauge theories . Springer DE, 2005, ISBN 978-3-540-23145-5 , p. 221– (accessed on January 31, 2013).
4. ↑ Gernot Münster: Quantum Theory . Walter de Gruyter, January 31, 2010, ISBN 978-3-11-021528-1 , p. 23– (accessed on January 31, 2013).
5. ↑ Charles Kittel: Introduction to Solid State Physics . Oldenbourg Verlag, 2006, ISBN 978-3-486-57723-5 , p. 35– (accessed on January 31, 2013).