On stable sector in supermembrane matrix model Original Research Article

We study the spectrum of SU(2)×SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constrains and single out the quantum number n (the Lorentz angular momentum). Energy levels are four-fold degenerate with respect to n and are labeled by nq , the largest n in a quartet. The Schrödinger equation is reduced to two different systems of two-dimensional partial differential equations. The choice of a system is governed by nq . We present the asymptotic solutions for the systems deriving thereby the asymptotic formula for the spectrum. Odd nq are forbidden, for even nq the spectrum has a continuous part as well as a discrete one, meanwhile for half-integer nq the spectrum is purely discrete. Taking half-integer nq one can cure the model from instability caused by the presence of continuous spectrum.