Bound states of the coupled‐channel Schrödinger equation: General eigenvalue function

Abstract

The eigenvalue problem for a system of N coupled one-dimensional Schrödinger equations, arising in bound state in quantum mechanics, is considered. A canonical approach for the calculation of the energy eigenvalues of this system is presented. This method replaces the use of the wave functions by 2N canonical functions having well-defined initial values at an arbitrary point r0. An eigenvalue function D(E) is associated with the system, where the energy E is considered as a variable. It is shown that the energy eigenvalues are the zeros of this function. This method is new in the sense that it reduces the eigenvalues search to that of finding the zeros of the function D(E), which is defined and constructed from the canonical functions independently from the wave function. A numerical application to a model problem proposed by Freidman et al. [Freidman, R. S.; Jamieson, M. J Comput Phys Commun 1989, 55, 137] is presented. It is shown that the eigenvalues computed by the present method are highly accurate for low and high levels; the average relative discrepancy between computed and exact one is about 1.5×10−11. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 325–332, 1999