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Recommended Textbook: Mathematical Methods for Physics and Engineering; Riley, Hobson and Bence, Chapters 1 and 3
Okay so the first bullet point is Trigonometric and hyperbolic functions; complex numbers. This is all one bullet point, for some reason, though I guess it's somewhat understandable.
The two big trigonometric functions are sine and cosine, written as . Read more > 
So, recently I learned that there is a standard undergraduate physics list of topics, called the Core of Physics and set by IoP.
Luckily, I know like half of that shit on there, and handily, there's a bunch of bullet points that each give convenient topic headings.
This means, of course, that I can churn out shitty blog posts, one to a heading, and when this is complete, we will all have degrees on this blessed day.
It's go time.
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Polyhedron69 has posted a very interesting blog post on the future of humanity, including transhumanism, posthumanism, and a speculative ultimohumanism. It’s a great blog post, and it’s recommended reading for this blog post.
I propose a different, but similar metric of xhumanism: where they are in mindspace.
Mindspace is an imaginary space in which minds lie. A “mind” is anything that produces models of the world and then performs actions based on predictions from that model; almost all humans have minds, as well as animals, and some artificial intelligences. Minds that are similar to each other are nearby in mindspace, and minds that are far away from each other are far away in mindspace.
A map of mindspace is to the left. You might notice…
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A hydrogen atom can be modeled as being made up of two point particles: a proton and an electron. These interact with each other electromagnetically (giving them potential energy), and also move around (giving them kinetic energy).
This means that the total energy can be written as
Just two operators left behind in it! We're almost there. We can separate out the wavefunction again, into an angular and a radial part.
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The language of quantum mechanics is the language of states and operators. They are closely related mathematical objects, and they're how the world works on its most fundamental level, so I hope you're listening closely.
A state is a configuration that your system can be in. A system is whatever you're doing the calculations on; in real life, there is only one system (the Universe), but physicists usually only look at very small subsystems, like single particles, when solving exactly. Fields like statistical and classical mechanics fill in the gap, generalising these smallscale quantum results to largescale results that are practically useful.
These configurations can be probability distributions. A valid state for a particle with spin mig…
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