What could be wrong with my approach to finding principal moments of inertia?

AI Thread Summary
The discussion revolves around the confusion regarding the calculation of principal moments of inertia for a discrete set of mass points on a plane. The user initially expresses concern about consistently obtaining a diagonal matrix for the inertia tensor when selecting a mass point as the origin. This raised doubts about the validity of their approach. Ultimately, the user resolves their confusion and acknowledges understanding the concept. The thread highlights the importance of correctly applying principles of inertia tensor calculations in physics.
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Homework Statement


I have a question on finding the principal moments of inertia of a discrete set of mass points on a plane. If I choose one of the mass points as the origin, I always end up having a diagonal matrix for the inertia tensor for any configuration. Isn't that weird? I sense something wrong with my solution. Could someone please help me?

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The Attempt at a Solution

 
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Never mind. I get it now guys.
 
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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