Since I’m in a good mood today and the majority of my peers skipped one of the most interesting courses.
1) Prerequisites. Integration, derivatives and partial derivatives should have been practiced ad nauseum at this point. A good grasp on linear algebra and basics of operators will also come in handy, as well as some complex analysis.
2) Classical mechanics. Yes, you have to know it, at least remember the basics, because it makes your life easier. Ideally, learn some Lagrange mechanics, since it teaches you to think in terms of energy rather than path. You’ll also need Coulomb’s law and centripetal acceleration for deriving Bohr’s atom model.
3) The first few chapters should be taught hand-to-hand with experiment and history. If your curiculum doesn’t provide this for some reason - go to youtube or even look experiments up on wikipedia. Learning concepts is easier when they are tied to real world at least in some way. At least know that Planck’s formula basically describes an oven.
4) The more advanced stuff will feel challenging. In the first part of the curriculum the sequence is always the same: make some assumptions about the system’s structure (e.g. electron in a potential well), from them obtain a hamiltonian, use Schrodinger’s equation to build a differential equation, then solve it using some gimmicks from differential equations course. The solution’s form is usually given in advance or supposed from the equation’s type.
5) Quantum mechanics is all about approximations: the only equations you will sovle precisely are for hydrogen atom and for an electron in some electrical or magnetic field. Everything else will imply some sort of approximation; learn them first, the rest can be derived.
2021-02-06, 09:00, Saturday
It is very satisfying to see a huge, long-time-in-the-making project come to an end. All the problems are solved, the code compiles and runs perfectly and displays validated output. Feels almost like defeating the strongest boss in a videogame, but without the bitter feeling of "ending", because there is no ending, at least not in my lifetime. Science is too vast to have one.
#stem #programming #life #coffeenotes
I am going through the process of creating my first video on youtube. This will probably be a series about thermodynamic modelling, which is a subject I am interested in. The question is: should I make it in matlab (which is easier for me and very fast) or in python (which is way too slow for anything serious but which more people know)? People of QOTO, what are your thoughts on the subject?
#STEM #help #question #thermodynamics #programming #matlab #python
2021-01-21, 08:22, Thursday. Drinking my morning coffee (cezve with some cinnamon) and preparing for my report. I'll probably make a separate post about it since it's an opportunity to tell about my scientific research. For now I'm in a mood to write some more "tips".
STEM tips №2: build your foundation. There is a very good reason for all textbooks on the same subject to convey material in the same order. It is not tradition, it is crucial for understanding concepts. The only exception in basic sciences I am familiar with is organic chemistry: Clayden's textbook is wildly diffirent from standart approach, but I'm not sure how it feels to actually use it for studying without prior knowledge of organic chemistry.
I digress. The particular order most textbooks follow builds new concepts on top of previous ones, and this principle applies throughout your academic career. Let's say you skipped a trigonometry introduction in high school. You crammed for the test and did fine, memorizing all your pi-over-2/3/4/6, but there is no solid understanding of the concept. Now you will struggle in your further math classes. Not only that, in mechanics knowledge of trigonometry is implied, the same applies for calculus, most of the physics and a bunch of other disciplines.
So the takeaway is: don't skip basic topics and make sure you know them very well. Otherwise your ignorance will backfire, usually sooner than later.
2021-01-22, 08:20, Friday. Plain black coffee with very high ratio, almost 10:1. I like it, though.
Yesterday I finished my fifth semester with science work report. Might as well write about my work here. So there are a lot of thermodynamic models of liquids. Modern ones are quite precise, but complicated and have a lot of maths involved. They are very useful to predict the reaction equilibrium or solution's properties, but because of their complexity you need to run them through computer. So people tend to create their own implementations of these models and use them, but diffirent implementations perform calculations slightly diffirently and this can affect results of the study.
The idea is to create a more or less versatile program with GUI, that would be easy to use by anyone and make results reproducible. I now managed to make a prototype with saving, loading and calculating quilibria. The core code of implementation is not mine, however, I use pre-coded model (my colleague made it) to create GUI and more or less intuitive logic around it. The entire thing is in C/C++ and runs quite smootly on binary systems.
2021-01-09, 07:30, Wednesday. Today I'll share some random thoughts on studying STEM related subjects. Might do somthing like this every once in a while.
STEM tips №1: there are no shortcuts. The original quote is attributed to Euclid: there are no royal roads to geometry, he said to king Ptolemey. This my point: you have to put in the hours and effort. A lot of them.
A decent problem in calculus or physics will take you a solid hour even if you have all the notes from your lectures. And there are these problems in every chapter of your textbook and they won't get easier, so cramming this kind of thing gets impossible. Unless your end goal is to pass the test and not to learn something.
I'm in the middle of my third year of bachelorship and there hasn't been a semester where I'd have more than a day off, unless I was ill. It doesn't mean that I always spend the whole day studying, although sometimes I do, but 1-2 hours of studying every morning are a part of my routine now.