Perturbation Theory for a Hamiltonian

[Cazicami]

Hi guys, this is my first time posting, I'm studying physics at uni, in my third year and things are getting a bit tough, so basically my question is in relation to solving problem 1, (i included a picture...) I missed the class and don't really know what I'm doing. Any help would be appreciated.

 

[HomogenousCow]

That's an elementary problem in peturbation theory, you can't expect us to explain everything here.
Just read over the chapter, there is a very nice formula for it.

 

[Cazicami]

Sorry to trouble you then.