Particle wave function

Does anyone have a calculation that can calculate a particle wave function over 1 planck time interval?

 

I think I may be asking the impossible. I am looking into the calculations for time dilation. I am wondering if the Planck values can be applied to reduce the scale of the calculations. I want minimal velocity values that reduce the movement to the microscopical level rather than the macroscopical. I am also looking at the Planck values as a definition of the speed of light.

 

I have just found information on the de Broglie frequency which answers my own question.