A wave packet of an harmonic oscillator.

(No, you are not seeing things. There really is a jerk when the particle returns to the center after a full period of physical motion, i.e. while going to the right again. The quantum solution is only periodic after two periods of physical motion, To avoid adding another megabyte to the file, the animation repeats after a physical period, not a quantum one. That means that the real part of the wave function, shown in red, will have a jump at the end of the physical period.)