An algorithm for the solution of the eigenvalue Schrödinger equation (Q915393)

A new algorithm is described for determining the eigenvalues of the one- dimensional radial Schrödinger equation of the form \(y''(r)=f(r)y(r),\) \(0<r<\infty\), where \(f(r)=U(r)-E,\) E is energy, \(U(r)=V(r)+\ell (\ell +1)/r^ 2.\) A new function \(z(r)=jy'(r)/y(r)\) named impedance is introduced [cf. the first and the second author, Comput. Phys. Commun. 43, 325-328 (1987; Zbl 0664.65091)]. Recursive formulas are obtained for \(y'(r^{n+1})/y(r^{n+1})\) in the cases \(U_ n-E\geq 0\) and \(U_ n- E<0.\) Absolute errors and real times of computation are tabulated for \(\ell =0\) and \(\ell =5\) using an optical potential and a Morse potential and compared with the results by \textit{Gh. Adam} [J. Comput. Phys. 22, 1- 33 (1976; Zbl 0329.65050)].