Exact diagonalisation of real-space, $D$-dimensional, $n$-component, possibly quasimomentum-dependent Hamiltonians $(H_{ij})$

$$\begin{align*} H_{ii}(\mathbf{x}) & =[-{\rm i}\delta\nabla-\mathbf{A}_{i}(\mathbf{x})+\mathbf{q}]^{2}+U_{ii}(\mathbf{x})-{\rm i}\tfrac{\Gamma_{i}}{2}\\\ H_{ij}(\mathbf{x}) & =U_{ij}(\mathbf{x}) \end{align*}$$

where

$$\begin{align*} & 1\leq i,j\leq n\\\ & \mathbf{x}=(x_{1},\ldots,x_{D})\\\ & \mathbf{A}_{i}(\mathbf{x})=(A_{i1}(\mathbf{x}),\ldots,A_{iD}(\mathbf{x}))\\\ & \mathbf{q}=(q_{1},\ldots,q_{D}) \end{align*}$$