COUPLED-CHANNEL METHODS FOR SOLVING THE BOUND-STATE SCHRODINGER-EQUATION

The coupled channel method for solving the bound-state Schrodinger equation is described. The method has been widely applied to the vibrational-rotational levels of floppy molecules such as Van der Waals complexes, but is also applicable in other areas of physics. It uses a basis set expansion for all degrees of freedom except a radial coordinate, and produces a set of coupled differential equations in the radial coordinate. In modern methods of solution, the coupled equations are solved by propagating the log-derivative of the wavefunction. Eigenvalues are located by searching for zeroes of: the determinant of the ''log-derivative matching matrix'' The resulting methods are very stable, and are the method of choice for providing eigenvalues to very high precision. Some recent advances in the methods, which provide improved convergence on eigenvalues and allow the calculation of wavefunctions, are described.