What are momentum,configuration and coordinate spaces?

[Joker93]

What is a momentum space,a coordinate space and a configuration space? Are they in classical or quantum mechanics or both? What are their similarities and differences and when,where and how are they used? thank you in advance!

 

[gtoguy97]

Momentum space is a space of momentum values associated with particles or fields. It is used in both classical and quantum mechanics and can be thought of as the space of possible momenta that particles can have. Momentum space is related to coordinate space, which is a space of coordinates that describe the positions of particles or fields. Coordinate space is also used in both classical and quantum mechanics.The main difference between momentum space and coordinate space is that momentum space is associated with the momentum of particles or fields, while coordinate space is associated with their position. Momentum space is typically used in computations involving the Hamiltonian formulation of classical mechanics or the Schrödinger equation in quantum mechanics, while coordinate space is used in computations involving the Lagrangian formulation of classical mechanics.Configuration space is also used in both classical and quantum mechanics. It is a space of all possible configurations of a particle or many particles and is used to describe the properties of a system. Configuration space is similar to coordinate space in that it involves coordinates to describe a system, but it includes additional information about the system, such as the relative positions of particles. All three spaces are used in both classical and quantum mechanics. They are used to describe the properties of a system and to solve equations governing the behavior of particles or fields. The similarities between them are that they all involve coordinates to describe a system, while the differences lie in the type of information they contain about a system.