Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed Calogero-Moser phase space'' of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some… Expand