  We study a real symmetric $\Phi^4$-matrix model whose kinetic term is given
by $\mathrm{Tr}( E \Phi^2)$, where $E$ is a positive diagonal matrix without
degenerate eigenvalues. We show that the partition function of this matrix
model corresponds to a zero-energy solution of a Sch\"odinger type equation
with Calogero-Moser Hamiltonian. A family of differential equations satisfied
by the partition function is also obtained from the Virasoro algebra.
