OPERATOR FORMULATION OF WIGNERS R-MATRIX THEORIES FOR THE SCHRODINGERAND DIRAC EQUATIONS

The R-matrix theories for the Schrodinger and Dirac equations are form ulated in the language of integral operators. In the nonrelativistic t heory the central role is played by an integral operator (R) over cap( (b) over cap)(E) relating function values to normal derivatives on a s urface L of a closed volume V, inside which the function satisfies the Schrodinger equation at energy E. In the relativistic theory, the sam e role is played by two integral operators, (R) over cap((b) over cap) ((+))(E) and (R) over cap((b) over cap)((-))(E), linking on the surfac e L values of upper and lower components of spinor wave functions sati sfying in the volume V the Dirac equation at energy E. Systematic proc edures for constructing the operators (R) over cap((b) over cap)(E) an d (R) over cap((b) over cap)((+/-))(E), generalizing the methods due t o Kapur and Peierls and to Wigner, are presented. (C) 1998 American In stitute of Physics. [S0022- 2488(98)00210-2].