Tensor product of Hilbert space When we are considering the total system as a composite system of two subsystems A and B, the wave functions of the composite system are in a Hilbert space H A ⊗ H B {\displaystyle H_{A}\otimes H_{B}} , if the Hilbert space of the wave functions for A and B are H A {\displaystyle H_{A}} and H B {\displaystyle H_{B}} respectively.