How to plot and animate an ODE in Maple using finite difference scheme

[Slide rule]

Hi,

I am currently trying to plot and animate a wave function using the Schrodinger equation.

I currently have the following finite difference equation:-

i(\psi(x, t+\Delta t)-\psi(x,t))/(\Delta t)=-(1/2)*(\psi(x+\Delta x, t)+\psi(x-\delta x, t)-2*\psi(x,t))/((\Delta x)^2)+V(x)*\psi(x,t)

Would I set x=-10, for example, where I plan to plot between -10 and 10 so the length L would be L=20 and \Delta x=L/N where N is the number of differences? Should I rearrange for \psi(x,t)?

As you can probably tell, I'm lost on what I need to do, any help or a similar example would be greatly appreciated.

Thanks

 

[Adrmay]

Yes, you can set x=-10 and plot between -10 and 10 so the length L would be 20 and \Delta x=L/N where N is the number of differences. You could rearrange the equation for \psi(x,t) to get a recursive relation for \psi(x,t+\Delta t) in terms of \psi(x,t). Then, you can use numerical methods (e.g. Euler method or Runge-Kutta method) to solve the equation numerically. You can then use the solution to plot and animate the wave function.