Griffiths QM Problem 6.9 Solution: THE BEST PROBLEM TO UNDERSTAND PERTURBATION THEORY

In this video I will solve problem 6.9 as it appears in the 3rd and 2nd edition of Griffiths Introduction to Quantum Mechanics. This is one of the best problems to understand perturbation theory
The problem states:
Consider a Quantum System with just three linearly independent states. The Hamiltonian in matrix form is ...
a) Write down the eigenvectors and eigenvalues of the unperturbed Hamiltonian
b) Solve for the exact eigenvalues of H. Expand each of them as a power series in epsilon, up to second order.
C) Use first- and second-order nondegenerate perturbation theory to find the approximate eigenvalue of the state that grows for the state that grows out of the nondegenerate eigenvector of H. Compare the exact result from b.
d) Use degenerate perturbation theory to find the first-order correction to the two initially degenerate eigenvalues. Compare the exact results.

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Explaining the problem
00:50 a) Finding the eigenvalues and eigenvectors
02:44 b) Finding the exact solutions
06:40 b) Approximating for small epsilon (Binomial theorem)
09:17 c) Finding corrections for E3
10:06 c) First order correction
12:36 c) Second order correction
18:07 d) Finding the degenerate corrections
19:20 d) Finding Waa, Wbb, Wab
22:04 d) Plugging them into E+- to find the result
24:18 Please support me on my patreon!

Correction:
08:15 I made a mistake multiplying here! The correct results are lambda+=V_0(2+epsilon^2) and lambda-=V_0(1-epsilon^2)