No commercial reproduction, distribution, display or performance rights in this work are provided. P17762.ĭiscrete Schrödinger operators, bound states, oscillation theory The one obtained from 2 has 12 supercharges with su(2)2 × u(1) and the other from 1 has 6 supercharges with u(1)3. DMS-0500910 and the Austrian Science Fund (FWF) under Grant No. Then a super Schrödinger subalgebra is found from each of them. This work was supported by the National Science Foundation under Grant No. Some remarks on the nonlinear Schrdinger equation in the critical case. Gerald Teschl gratefully acknowledges the extraordinary hospitality of the Department of Mathematics at Caltech, where this work was done. norm for some radial L 2 super critical non linear Schrdinger equations. Article electronically published on October 4, 2006. Received by the editors Septemand, in revised form, November 9, 2005. So check whether wave function is blowing up or not at infinity. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of the number of eigenvalues below a given energy as this energy tends to the bottom of the essential spectrum. Answer: If a general wave function is given, and to know whether it is a solution of the Schrodinger equation or not, Check the following three conditions: 1. We consider discrete one-dimensional Schrödinger operators whose potentials decay asymptotically like an inverse square.
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