Solving the general Schodinger equation

[KillaKem]

Equations are found at : http://www.viewdocsonline.com/document/zl3psf

3.Plot the expression for the Gaussian wavepacket, equation (2) of the notes
for t = 0; 0.5; 1.5 secs
Use N = 4096 L = 25 (length of positive x axis), beta = 0:5785 (an
electron),  alpha = 0.5, k0 = 1, x0 = L, xN = L, dx =
2L/N.

4.Write and test the symmetric tridiagonal system of equation solver in C#. Adapt
the code from the notes for use with your complex number types.

5.Repeat 3 by evolving psi(x, 0) in time by solving equations (7), (9) and (10)
in the notes using your solver from 4. above. I used t = 0.001. Note V (x)
from the notes is 0 everywhere in this part but include it in you program
because you need it for the next bit


What I don't understand is the fifth question, what do they mean by "evolve in time"? I thought it meant to plot psi(x,t) for different values of t but how can that be possible if they have already given me that t = 0? Even if I did that i would need values of R in order to solve for the psi vector, where do I get that? Can somebody explain to me what question 5 wants me to do, I am not a Physicist so very complex explanations will probably not be understood.

 

[mfb]

I thought it meant to plot psi(x,t) for different values of t but how can that be possible if they have already given me that t = 0?

You are supposed to calculate it for other values of t.

I think you do not need the R_i, the equations are all "something with psi = R_i = some other thing with psi".

 

[KillaKem]

You are supposed to calculate it for other values of t.

I think you do not need the R_i, the equations are all "something with psi = R_i = some other thing with psi".

I think I have to find a way of getting values of R because I need to substitute them in equation 11 in order to get the value of psi.I really still don't understand what's going on in this question.If I need to evolve psi(x,0) then that means I will have to plot psi(x,0), psi(x,0.5) and psi(x,1.5) by solving equations (7), (9) and (10).

Now as an example, for psi(x,0) I know :

psi(x,t) = psi(j*dx,n*dt)

=> x = j*dx and n*dt = 0, where dt = 0.001, -4096 < j < 4096, -25 < x < 25

But how do I use this information to plot the graph of psi(x,0)?