  This paper proves an analogue of a result of Banuelos and Sa Barreto on the
asymptotic expansion for the trace of Schrodinger operators on $\R^d$ when the
Laplacian $\Delta$, which is the generator of the Brownian motion, is replaced
by the non-local integral operator $\Delta^{\alpha/2}$, $0<\alpha<2$, which is
the generator of the symmetric stable process of order $\alpha$. These results
also extend recent results of Banuelos and Yildirim where the first two
coefficients for $\Delta^{\alpha/2}$ are computed. Some extensions to
Schrodinger operators arising from relativistic stable and mixed stable
processes are obtained.
