Jeremy Côté

Bits, ink, particles, and words.

Degeneracy of the Quantum Harmonic Oscillator

Note: This post uses MathJax for rendering, so I would recommend going to the site for the best experience.

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Being Happy With Being Repetitive

One of the most difficult things to do in life is to focus. Maybe you’re different than me, but I have a lot of trouble sitting down and focusing on one task or idea. Instead, my mind buzzes with activity while my hands do another. I’m always switching between ideas, and it takes a lot of energy to focus on just one.

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Peeling Back the Onion

No matter how much advanced mathematics you study, the great thing is that you rarely have to accept anything as-is. If you come across a procedure, technique, or result and you wonder how in the world it works, you can always retrace your steps and get back to the foundational reasons as to why it works. If you keep on asking “why”, you will eventually get back to your starting axioms. In between that and your starting point, you should be able to understand the concept as obvious1.

  1. Though, retracing the steps of a proof or technique can be a lot trickier than you initially bargained for. 

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How Many People Need To Watch?

We like being recognized for the work we do. This is even more relevant now, with the idea of documenting everything you do. (If it isn’t documented, did it happen?) We don’t want to do work unless there is some reward attached.

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