Abstract: In μ space，classical mechanics and quantum mechanics provide，respectivley，two seemingly different

and actually equivalent descriptions for one-dimensional free particles. There are some errorous presentations in

some classic textbooks，and completed results are elucidated.In this paper，the trajectories of μ space are plotted

with analyzing the motion of free particles in a one-dimensional box and in full space in classical mechanics，respectivley.

Then，with examining particle motion in quantum mechanics under the condition of periodic boundary in full space and in an infinite depth well respectivley，we show that the same area element is occupied by each quantum state in μ space，irrespective of the different methods taken.Two related problems，the existence of the quantum state of zero-momnentum and relationship between the Heisenberg uncertainty principle and the area element for a quantum state to accommodate，are re-visited.

Key words: statistical physics, classical states, quantum states, μ space