Internal eigenstate problem: The trial state method - art. no. 026701

It is shown that the device of adding a special trial state to a basis set, thus augmenting by 1 the dimension of any complex matrix being studied, le ads to a formalism that permits the application of the wave operator approa ch to calculating the internal spectrum of the matrix as well as the action of the resolvent operator (E -H)(-1) on an arbitrary vector in the origina l N-dimensional space. Two calculational variants of the method are describ ed and both are tested by studying the problem of a shea laser pulse intera cting with a H-2(+) ion.