A NEW METHOD FOR DETERMINING EXCITED-STATES OF QUANTUM-SYSTEMS

A new method for computing excited states of a given operator H is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state of H nearest in energy to any chosen trial energy E(t), we consider the auxillary operator A = (H - E(t))2. We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces for A is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state of A is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed.