Spiky membranes

We study spiky configurations of membranes in the SO(d)×SU(N) invariant matrix models. A class of exact solutions (analogous to plane-waves) of the corresponding Schrödinger equation for an arbitrary N is discussed. If the large N limit is performed so that the energy scales like N2, the N=∞ wavefunctions reduce to the ground state of the d-dimensional harmonic oscillator.