Defining the Hamiltonian

The Hamiltonians that can be treated by the MCTDH-X package in its current implementation are those with maximally two-body operators. In general such a Hamiltonian hence contains the kinetic energy $\hat{T}$ and the external potential $\hat{V}$ and an interparticle interaction $\hat{W}$:

$$\hat{H}=\sum_{i=1}^N (\hat{T}_i+\hat{V}_i) + \sum_{i<j=1}^N \hat{W}_{ij}.$$ (1)

To fully define this Hamiltonian in dimensionless units [see Phys. Rev. A 77, 033613 (2008)] one has to define the one-body potential $\hat{V}$, and the two-body interaction $\hat{W}$. It has to be stressed, that both operators can be in principle time-dependent.