qsolver: A program for the accurate solution of coupled radial Schrödinger equations for bound and resonant states
Description
The Fortran program qsolver is designed to solve a system of coupled radial Schrödinger equations for both bound and resonant (quasi-bound) energy levels. To search for energies and widths of resonant states, the program utilizes the exterior complex scaling method. The potential-energy matrix V(r) and the optional radial-coupling matrix B(r) are supplied by the user as either real or complex functions of the radial coordinate r. For resonant-state calculations qsolver can also automatically extrapolate the real-valued multiplicative Vmn(r) and Bmn(r) functions into the complex plane. An exact analytical transformation 𝑥=𝑓(𝑟) maps the modified coupled-channel (CC) equations from a semi-infinite r ∈ [a, ∞) or infinite 𝑟 ∈ (−∞,+∞) interval onto a finite domain x ∈ [a, b], enabling their numerical solution via polynomial collocation methods that exhibit an exponential convergence rate. The program is able to identify spurious (”ghost”) resonant states by examining their eigenfunctions in a spectral basis as well as to evaluate partial derivatives of both real and complex eigenvalues with respect to Hamiltonian parameters, including the reduced mass μ. Built around a modern Fortran 2003 interface in which most arguments are optional, qsolver is straightforward to use and to incorporate into the user’s code. The qsolver program can effectively find energies and widths of the resonant states with an accuracy of up to 13-14 significant digits in double-precision (real*8) arithmetic, as confirmed by numerical tests.