Given a Hamiltonian, find eigenvalues and eigenvector

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To find eigenvalues and eigenvectors of a Hamiltonian, users must first provide their own work and thoughts on the problem, as per forum rules. Key concepts include understanding matrix representations of operators, hermitian operators, eigenvectors, eigenvalues, commutators, and projectors. Participants are encouraged to engage with these foundational topics to facilitate assistance. The discussion emphasizes the importance of following forum guidelines to receive help. Overall, sharing initial efforts is crucial for collaborative problem-solving in this context.
mudyos
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Problem :

in
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what have you done and though so far? If you don't tell us and show us, you'll get no help-
 
mudyos: This forum works as this: You post question and work and thougts done. If not, then no one will help you. The RULES of this forum is those, didn't you read the rules before posting here?

I give you some questions for you to answer, then maybe you can do something.

What is a matrix representation of an operator?
What is an hermitian operator and matrix?
What is an eigenvector and eigenvalue?
What is a commutator?
What is a projector?
 
I'm not about to download a .doc file.
 
thes is Attach File
 

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It doesn't matter christianjb and mudyos. Follow the rules and show work.

mudyos: why can't you answer my questions?
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
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