Relativistic SUSY QM as Deformed SUSY QM

The relativistic finite-difference SUSY Quantum Mechanics (QM) is developed. We show that it is connected in a natural way with the q-deformed SUSY Quantum Mechanics. Simple examples are given. The relativistic QM is based on Snyder’s idea of noncommutative space-time coordinates and the concept of relativistic configurational space. We refer the reader to the review papers [1-5], and the references therein. The natural connection of RQM with q-deformations is discussed in the articles [5, 6]. The one-dimensional relativistic Schr¨odinger equation has the form