How can I plot time-dependent wave-functions?

  • #1
I am trying to plot the wave-function of free particles as a function of x and time. Can someone explain or reference a site which explains how.

--Thank you
 

Answers and Replies

  • #2
RaulTheUCSCSlug
Gold Member
179
25
So for this, it will be helpful if you understand a bit of multivariable calculus. Since the plot will not only be a function of time, but also a function of space (x,t) so your function now has two variables. We know this for a fact, because we encounter it in our daily lives. (at least we perceive it to be such a fact) Now looking at standard equation of a wave :
wavdes2.gif

We see how a function might change as x, and t changes. But much of the time, one parameter may seem rather arbitrary, and that parameter may be time.

I know that I am getting a bit off topic, but use the standard equations of a wave to guide you on what you want to plot. I believe Wolfram alpha has the ability to plot functions of several parameters if I am not mistaken. Experiment, and have a little fun with it. :)
 
  • #3
So for this, it will be helpful if you understand a bit of multivariable calculus. Since the plot will not only be a function of time, but also a function of space (x,t) so your function now has two variables. We know this for a fact, because we encounter it in our daily lives. (at least we perceive it to be such a fact) Now looking at standard equation of a wave :
wavdes2.gif

We see how a function might change as x, and t changes. But much of the time, one parameter may seem rather arbitrary, and that parameter may be time.

I know that I am getting a bit off topic, but use the standard equations of a wave to guide you on what you want to plot. I believe Wolfram alpha has the ability to plot functions of several parameters if I am not mistaken. Experiment, and have a little fun with it. :)

Raul,

Thanks, and yeah I have been trying to plot the Solution to the Schrödinger equation for a free particle using Wolfram they have an interactive option where you can play around with the wave. However when plotting
$$\Psi(x,t)=e^{ikx-wt}$$
and I have x fixed, the real and imaginary components do not oscillate vertically with time. Maybe Python will do the trick?

--Freddy Cisneros
 
  • #4
RaulTheUCSCSlug
Gold Member
179
25
Raul,

Thanks, and yeah I have been trying to plot the Solution to the Schrödinger equation for a free particle using Wolfram they have an interactive option where you can play around with the wave. However when plotting
$$\Psi(x,t)=e^{ikx-wt}$$
and I have x fixed, the real and imaginary components do not oscillate vertically with time. Maybe Python will do the trick?

--Freddy Cisneros

Damn, yeah maybe python can do the trick, or C. But that goes beyond the realm of my knowledge.
 
  • #5
Damn, yeah maybe python can do the trick, or C. But that goes beyond the realm of my knowledge.

Thanks Raul, I'll look into it a little deeper.

--Freddy Cisneros
 
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