On the convergence of splitting methods for linear evolutionary Schrodinger equations involving an unbounded potential

In this paper, we study the convergence behaviour of high-order exponential operator splitting methods for the time integration of linear Schrodinger equations i partial derivative(t) psi(x, t)=-1/2 Delta psi(x, t)+ V (x)psi(x, t), x is an element of R-d, t >= 0, involving unbounded potentials; in particular, our analysis applies to potentials V defined by polynomials. We deduce a global error estimate which implies that any time-splitting method retains its classical convergence order for linear Schrodinger equations, provided that the exact solution of the considered problem fulfills suitable regularity requirements. Numerical examples illustrate the theoretical result.