This code solves time-dependent one-dimensional Schrödinger Equation with finite difference Crank-Nicolson method for Gaussian wave packet. The real and imaginary parts of the wave function are shown on a complex plane.
Details of the calculation: Goldberg, Abraham, Harry M. Schey, and Judah L. Schwartz. "Computer-generated motion pictures of one-dimensional quantum-mechanical transmission and reflection phenomena." American Journal of Physics 35, no. 3 (1967): 177-186. https://ergodic.ugr.es/cphys/lecciones/SCHROEDINGER/ajp.pdf Press, William H. Numerical recipes 3rd edition: The art of scientific computing. Cambridge university press, 2007. §20.2.1 Schrödinger Equation.