A variable‐step procedure for the numerical integration of the one‐dimensional Schrödinger equation Free

Two P‐stable methods with phase lag of order 10 and 12 are developed in this paper for the numerical integration of the one‐dimensional Schrödinger equation. Based on a new local error, the local phase‐lag error (LPLE), a new variable‐step procedure is produced. Numerical results indicate that the new variable‐step method is more efficient than the similar well‐known variable‐step procedure of Raptis and Cash [Comput. Phys. Commun. 1985, 36, 113–119 (1985)].