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

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