In quantum mechanics, the point particle is replaced by a quantum wave packet and the divergence problem is naturally avoided. To the lowest-order Magnus expansion for Floquet system, the quantum phase space interaction of two particles is the time-averaged real space interaction over the periodic two-body quantum state Φ Φ ( x i , x j , t ) as follows. U i j = 1 T ∫ ∫ 0 T ⟨ ⟨ Φ Φ ( x i , x j , t ) | V ( x i − − x j ) | Φ Φ ( x i , x j , t ) ⟩ ⟩ . In the coherent state representation, the quantum phase space interaction approaches the classical phase space interaction in the long-distance limit. For N bosonic ultracold atoms with repulsive contact interaction bouncing on an oscillating mirror, it is possible to form Mott insulator -like state in the Z n phase space lattice. In this case, there is a well defined number of particles in each potential site which can be viewed as an example of 1D many-body phase space crystal.