The Discrete Bound State Spectrum of the Rotating D0-brane System

In this note we obtain the discrete spectrum of the rotating ellipsoidal membrane, the solution to classical equations of motion in the matrix mechanics of N D0-branes. This solution has the interpretation of a closed D2-brane with the D0-branes bound to its surface. The semi-classical quantization is performed on the rotational modes with the result that both radii and energy are quantized. We also argue that the quantum mechanics of this system is well defined, with a unique ground state of positive energy in each sector with a non-zero angular momentum. The scaling of the size and energy of these states allows us to identify our rotating brane excited states with the previously conjectured resonances in the scattering of D0-branes.