Prove or disprove the following proposition:

For any smooth plane vector field $\mathbf{H}=\left(H\_x,H\_y\right)$, there exist scalar potentials $\phi$, $\psi$ such that

$H\_x=\frac{\partial \phi }{\partial x}+\frac{\partial \psi }{\partial y}$

$H\_y=\frac{\partial \phi }{\partial y}-\frac{\partial \psi }{\partial x}$