On the approximation of the solution of the Schrodinger equation by superpositions of stationary solutions

Lot S be a symmetric operator with gap J. Suppose in addition that the deficiency indices of S are infinite, the Hamiltonian H is a self-adjoint extension of S and the support of the spectral measure mu(f0,H) of the initial state f(0) is a compact subset of J. Then there exist other self-adjoint extensions H-n of S and finite sums f(n) of eigenvectors of H-n such that c(-itHn)f(n)-->c(-itH)f(0), as n --> infinity, locally uniformly in time. Upper estimates for the rate of convergence will be given.