What is a phase space? - Physics Stack Exchange What is a phase space? And can the phase space be specified with x and y instead of with theta and omega? I am currently working on a problem where I am graphing the trajectories of three masses (the three-body problem) Is the plot of their superimposed trajectories (x vs y in space, no z as the angular momentum is zero) considered a phase space?
Phase space in classical mechanics - Physics Stack Exchange Finally, the phase space can be made of dimensions other than positions and velocities It is very common to describe the system in terms of positions and momenta, or include spins, etc The common feature is finding what are the minimal necessary quantities necessary to describe the system, and those will be the dimensions of the phase space
What does the concept of phase space mean in particle physics? The phase space is just the mathematical space of all possible momenta of all the outgoing particles As a very simple example, consider $\mathrm{e}^-\mathrm{e}^+\to\gamma\gamma$ At LEP , each of the electron and positron would have a momentum of $104 5\text{ GeV} c$, which means each of the photons would have essentially that same magnitude
What is Phase Space Formulation of QM and does it explain use of . . . In arXiv:quant-ph 0504102, A J Bracken says if we think of the phase space formulation of QM as more fundamental, arising directly from a deformation of classical mechanics in phase space [12] we can think of the formulation of QM in Hilbert space and the associated introduction of complex numbers as a computational device to make calculations easier
How is Phase Space defined in Statistical Mechanics? You could, if you liked, imagine an n-dimensional space to keep track of the individual positions of n people along the path, which would be represented by a single point moving in the n-dimensional space Phase space is a similar idea- to keep track of the coordinates of n particles moving in 3 dimensional space, you have a single point moving
What is the difference between configuration space and phase space? The velocity phase space is not, in general, a symplectic manifold To be able to ascertain how the phase flow transforms a volume, you need to have a structure that defines volume, which in the momentum phase space, the symplectic form does, while in the velocity phase space, there is no such canonical structure
classical mechanics - Physical Interpretation of Phase Space Volume . . . Perhaps one of the most important results of the whole of Classical Mechanics is that the volume occupied by an ensemble in the phase space remains constant in time Another very interesting result is that it is also invariant under canonical transformations (as the Jacobian of the canonical transformation is generically unity)
What is the purpose of phase space? - Physics Stack Exchange Define phase space: In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space For mechanical systems, the phase space usually consists of all possible values of position and momentum variables
classical mechanics - Volume as a choice of measure in phase space . . . Finally, a more specific question: in the context of dynamical systems and discussions of accessibility of different parts of phase space, it is often said that almost all points in the space are accessible, except for a set of measure zero initial conditions (points)
How does one quantize the phase-space semiclassically? Now you notice that the area in phase space is invariant under canonical transformations (for infinitesimal canonical transformations this is Liouville's theorem), so that the area between the orbits at J and J+dJ is the same as the area in x-p coordinates between J and J+dJ, which is just dJ because that's the definition of J