It's Obvious... Not: Knowing When not to do the Math

I'm still studying for quals. I got stuck for awhile on problem 2.11 of Griffith's Introduction to Quantum Mechanics first edition. The problem involves manipulating raising and lowering operators to perform a normalization. The problem I was having was doing too much of the math too early. I tried to expand all the operators and got stuck. I tried to apply integration by parts as the book suggests and applied it to the wrong term the first time, and carried the operation too far on a second try. The series of conservative steps that finally did the trick is shown in the video below.

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The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1. While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero. This is typically explained in the following way. While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare. That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2]. Cabrera was utilizing a loop type of magnetic monopole detector. Its operation is in...

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More Cowbell! Record Production using Google Forms and Charts

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