Factorization method on time scales

We present an approach to the factorization method for second order difference equations on time scales. We construct Hilbert spaces of functions on the time scale and show how to construct a chain of intertwined first order $\mathrm{\Delta }$-difference operators ${\mathcal{A}}_k$ in the sense that ${\mathcal{A}}_k$ and ${\mathcal{A}}_k^{\ast }$ act as ladder operators generating new solutions of eigenproblem of ${\mathcal{A}}_k{\mathcal{A}}_k^{\ast }$.