TY - JOUR T1 - The Fundamental Gap for a Class of Schrödinger Operators on Path and Hypercube Graphs JF - Journal of Mathematical Physics Y1 - 2014 A1 - Michael Jarret A1 - Stephen P. Jordan AB - We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schr\"{o}dinger operator acting on a class of graphs. In particular, we derive tight bounds for the gap of Schr\"{o}dinger operators with convex potentials acting on the path graph. Additionally, for the hypercube graph, we derive a tight bound for the gap of Schr\"{o}dinger operators with convex potentials dependent only upon vertex Hamming weight. Our proof makes use of tools from the literature of the fundamental gap theorem as proved in the continuum combined with techniques unique to the discrete case. We prove the tight bound for the hypercube graph as a corollary to our path graph results. VL - 55 U4 - 052104 UR - http://arxiv.org/abs/1403.1473v1 CP - 5 J1 - J. Math. Phys. U5 - 10.1063/1.4878120 ER -