Discrete energy representation and generalized propagation of physical systems

This work discusses the discrete energy representation based on generalized propagation of a physical system. Here, the propagation is defined as a recursion scheme which generates a series of system states from a given initial state. Examples of such schemes include the time propagation and polynomial recursion. It is argued that each propagation determines a set of energy points, which form the discrete energy representation. A unitary transformation can be established between the discrete energy representation and the generalized time representation, much like the well-known transformation between the discrete variable representation and the finite basis representation. Such a collocation approach can be useful in calculating many properties that are local in the energy domain. Numerical examples are presented to demonstrate the utility in filter diagonalization. (C) 1998 American Institute of Physics. [S0021-9606(98)02815-3].