Near-resonant excitation of a two-level system

[krootox217]

Homework Statement

Hello, I have the following task:

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Homework Equations

In the task[/B]

The Attempt at a Solution

I looked at this task with the notes from the class, but I can't really see through. It seems that the first step is the transformation into the single decoupled second order differential equation, but I don't actually understand how to do that and at which point I need a program to solve it. Can someone guide me through the solution process?

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[DrClaude]

Write the two equations for $\dot{c}_0$ and $\dot{c}_1$ and derive both sides with respect to time. It shouldn't be too hard to see then how to obtain the two uncoupled equations.

 

[krootox217]

Hello,
thank you for helping me.

I tried to do that and obtained the following:

If this is correct, I still don't see what I have to do in the next step and when I have to use a program.