Piecewise Constant Perturbation Methods for the Multichannel Schrödinger Equation

The CPM{P,N} methods form a class of methods specially devised for the propagation of the solution of the one-dimensional Schrodinger equation. Using these CPM{P,N} methods in a shooting procedure, eigenvalues of the boundary value problem are obtained to very high precision. Some recent advances allowed the generalization of the CPM{P,N} methods to systems of coupled Schrodinger equations. Also for these generalised CPM{P,N} methods a shooting procedure can be formulated, solving the multichannel bound state problem.

[1]  B. R. Johnson.  The renormalized Numerov method applied to calculating bound states of the coupled‐channel Schroedinger equation , 1978 .

[2]  L.Gr. Ixaru.  LILIX—A package for the solution of the coupled channel Schrödinger equation☆ , 2002 .

[3]  J. W. Cooley,et al.  An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields , 1961 .

[4]  J. Hutson.  Coupled channel methods for solving the bound-state Schrödinger equation , 1994 .

[5]  Guido Vanden Berghe,et al.  MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations , 2005, TOMS.

[6]  A. C. Allison.  The Numerical Solution of the Equations of Molecular Scattering , 1989 .

[7]  C. R. Bingham,et al.  Proton emitters 140 Ho and 141 Ho : Probing the structure of unbound Nilsson orbitals , 1999 .

[8]  H. De Meyer,et al.  SLCPM12 - A program for solving regular Sturm-Liouville problems. , 1999 .

[9]  Guido Vanden Berghe,et al.  CP methods of higher order for Sturm-Liouville and Schrödinger equations , 2004, Comput. Phys. Commun..

[10]  H. De Meyer,et al.  CP methods for the Schro¨dinger equation revisited , 1998 .

[11]  R. Levine.  Adiabatic approximation for nonreactive, subexcitation, molecular collisions. , 1968 .

[12]  A. C. Allison,et al.  The numerical solution of coupled differential equations arising from the Schrödinger equation , 1970 .

[13]  Guido Vanden Berghe,et al.  CPM{P, N} methods extended for the solution of coupled channel Schrödinger equations , 2006, Comput. Phys. Commun..

[14]  Roy G. Gordon,et al.  New Method for Constructing Wavefunctions for Bound States and Scattering , 1969 .

[15]  Liviu Gr Ixaru,et al.  Numerical methods for differential equations and applications , 1984 .