Supersymmetry in quantum mechanics with point interactions

We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N = 2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N = 2 supercharges. Spontaneous supersymmetry breaking due to point interactions and an extension to higher N-extended supersymmetry are also discussed. (C) 2003 Elsevier Science B.V. All rights reserved.