According to classical Mechanics, Hamiltonian is the function of position and momentum. So we can describe motion of classical particles in position space and momentum space (phase space)
The path followed by a particle in phase is known as phase trajectory.
But in quantum mechanics the concept of phase trajectory is not valid due to uncertainty principal i.e both positions and momentum cannot be calculated simultaneously. So we can describe motion of particle separately in position space and momentum space.
If We Know the motion of particle in positions space then we describe it in momentum space using Fourier transform
Let f(x) is function define in position space for all values of x, then using fourier transform we get it in momentum space i.e
Also we can return back from momentum space to position space by taking Fourier inverse transform.
