SIEGERT PSEUDOSTATE FORMULATION OF SCATTERING-THEORY - ONE-CHANNEL CASE

Siegert pseudostates (SPSs) are defined as a finite basis representati on of the outgoing wave solutions to the radial Schrodinger equation f or cutoff potentials and the problem of their calculation is reduced t o standard linear algebra easily implementable on computers. For a suf ficiently large basis and the cutoff radius, the set of SPSs includes bound, weakly antibound, and narrow complex-energy resonance states of the system, i.e., all the physically meaningful states observable ind ividually. Moreover, the set is shown to possess certain orthogonality and completeness properties that qualify it as a discrete basis suita ble for expanding the continuum. We rederive many results of the theor y of Siegert states in terms of SPSs and obtain some (to our knowledge ) previously unknown relations. This not only makes the results practi cally applicable, but also sheds a new light on their mathematical nat ure, In particular, we show how the Mittag-Leffler expansions for the outgoing wave Green's function and the scattering matrix can be obtain ed on the basis of very simple algebraic relations, without assuming t hem to be meromorphic functions. Explicit construction of these two fu ndamental objects completes the SPS formulation of scattering theory f or the one-channel case. The computational efficiency of this approach is illustrated by a number of numerical examples.