Higher-Order Derivative Susy in Quantum Mechanics with Large Energy Shifts

Abstract

Within the framework of second order derivative (one dimensional) SUSYQM we discuss particular realizations which incorporate large energy shifts between the lowest states of the spectrum of the superhamiltonian (of Schr\"odinger type). The technique used in this construction is based on the "gluing" procedure. We study the limit of infinite energy shift for the charges of the Higher Derivative SUSY Algebra, and compare the results with those of the standard SUSY Algebra. We conjecture that our results can suggest a construction of a toy model where large energy splittings between fermionic and bosonic partners do not affect the SUSY at low energies.