What is Configuration space: Definition and 15 Discussions

In mathematics, a configuration space is a construction closely related to state spaces or phase spaces in physics. In physics, these are used to describe the state of a whole system as a single point in a high-dimensional space. In mathematics, they are used to describe assignments of a collection of points to positions in a topological space. More specifically, configuration spaces in mathematics are particular examples of configuration spaces in physics in the particular case of several non-colliding particles.

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  1. Pradyuman

    A Wave-packet in configuration space

    In the book "Group theory and it's Applications to the Quantum Mechanics of atomic spectra " by Eugene P. Wigner in chapter 4 The elements of quantum mechanics it is written What does the wave-packet and the refractive index implies here.How to interpret this?
  2. L

    I Can configuration space be observer independent?

    We can formulate the spacetime in an observer/coordinate independent way, i.e. a particle becomes a worldline in the 4d space. Then relative to each observer, the worldline can be casted to a function in R^3. However, I haven't found any reference on formulating configuration space in a...
  3. A

    A Does Antony Valentini's "sub-quantum measurement" really work?

    In https://arxiv.org/pdf/quant-ph/0203049.pdf, which is in the realm of Bohmian mechanics, Antony Valentini claims that by having a "non-equilibrium" particle with arbitrarily accurate "known" position, we can measure another particle's position with arbitrary precision, violating Heisenberg's...
  4. sams

    A Difference between configuration space and phase space

    Lagrangian Mechanics uses generalized coordinates and generalized velocities in configuration space. Hamiltonian Mechanics uses coordinates and corresponding momenta in phase space. Could anyone please explain the difference between configuration space and phase space. Thank you in advance for...
  5. J

    Classical mechanics: Jacobi variational principle

    An isolated mechanical system can be represented by a point in a high-dimensional configuration space. This point evolves along a line. The variational principle of Jacobi says that, among many imagined trajectories between two points, only the SHORTEST is real and is associated with situations...
  6. F

    Motivation for Lagrangian mechanics

    I know how to implement Lagrangian mechanics at a mathematical level and also know that it follows the approach of calculus of variations (i.e. optimisation of functionals, finding their stationary values etc.), however, I'm unsure whether I've grasped the physical intuition behind the...
  7. Matta Tanning

    Relation between phase space and path integral formulation?

    I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with quasi-probability distributions on the phase space and the path integral formulation usually deals with a sum-over-paths in the configuration space. I see how they both lead...
  8. bohm2

    The reality of Configuration space

    Someone suggested to me that this stuff may be more appropriate in the QM section (I’m not sure?). I think others on here have brought this up before but I thought I’d post some stuff I’ve come across that may be useful to some as a kind of an introductory reading on the ontology of...
  9. D

    Configuration Space In Classical Mechanics: Definition

    Hi, I'm a bit confused wit the concept Configuration Space. First, the professor defined generalised coordinates as such: U got a system of n particles, each particle has 3 coordinates(x,y,z), so u got 3n degrees of freedom. If the system has k holonomic constraints, u got 3n-k degrees...
  10. A

    How to go from the configuration space to the phase space?

    How can we go from the configuration space of the system to the phase space when velocity can be expressed in terms of momenta?
  11. N

    What is Configuration Space in Quantum Mechanics?

    In a section describing "Problems Raised by Statistical Interpretation" of the Schrodinger wave equation, Albert Messiah (QUANTUM MECHANICS) says this: Huh? I assume he is referring to psi (r,t) which he originally introduced almost 100 pages earlier this way: This seems "concrete"...
  12. quasar987

    What is a configuration space?

    I keep reading that the configuration space of a given system is the "space of all it's posible positions". Along with this is the inevitable example that the configuration space of a double pendulum is the 2-torus, S^1 x S^1. This makes sense: the possible positions of the first bob is a circle...
  13. Demystifier

    Configuration space vs physical space

    The question (or puzzle) that I want to pose essentially belongs to classical (not quantum) physics. Nevertheless, there is a reason why I post it here on the forum for quantum physics, as I will explain at the end of this post. As a simple example, consider the following Hamiltonian...
  14. jal

    The Quantum Configuration Space of Loop Quantum Cosmology

    Hi marcus! It seems to me that there are many different approaches, from around the world, that are converging at an accelerated pace. Maybe not? … It might just be my desire to understand minimum length. http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.2397v1.pdf The Quantum Configuration...
  15. S

    Deriving the Quantum Properties of a General Configuration Space

    The requirements, posed on a system given by the configuration coordinates q(t) = (q^1(t), q^2(t), ...) that (1) they be subject to 2nd-order equations of motion: q'(t) = v(t), v'(t) = a(q(t),v(t)) and (2) have a classical configuration space at each time: [q^i(t), q^j(t)] = is nearly...