Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrodinger equations

Some embedded Runge-Kutta methods for the numerical solution of the eigenva lue Schrodinger equation are developed. More specifically, a new embedded m odified Runge-Kutta 4(6) Fehlberg method with minimal phase-lag and a block embedded Runge-Kutta-Fenlberg method are developed. For the numerical solu tion of the eigenvalue Schrodinger equation we investigate two cases. (i) T he specific case, in which the potential V(x) is an even function with resp ect to x. It is assumed, also, that the wavefunctions tend to zero for x -- > +/-infinity. (ii) The general case for the well-known cases of the Morse potential and Woods-Saxon or Optical potential. Numerical and theoretical r esults show that the new approaches are more efficient compared with the we ll-known Runge-Kutta-Fehlberg 4(5) method.