On Stable Sector in Supermembrane Matrix Model

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.