Learning Quantum Mechanics correctly
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Quoted By: >>12393986 >>12394924 >>12395037 >>12398181
A bit of background: physics undergrad starting graduate quantum mechanics.
I took a standard year-long undergrad course (using the griffiths book) that started with the Schrodinger equation, wavefunctions, and then followed by approximation techniques. Somewhere in the middle of all of that, they awkwardly shoehorned Dirac notation and the mathematical postulates.
I was able to solve the problems, but I could never holistically wrap my mind around the structure theory. In other words, I could not articulate the reasons for why things were done in the way that they were. Turns out that starting out with wave mechanics is a terrible route. It is a special case of the more general theory, mainly convenient for calculating continuous quantities in a few practical models. But it does not teach intuition well! It is too easy to muddle in classical intuition when the curriculum presents this first. The real intuition comes from seeing how the constraints of probability under time evolution necessitate the use of complex vector spaces, eigenbasis, hermitian operators, etc. to elegantly calculate values. I found a helpful set of videos for anyone in a similar position. They have a fairly low view count for their quality, perhaps because they assume you already have some background:
https://www.youtube.com/c/ProfessorMdoesScience/videos
I took a standard year-long undergrad course (using the griffiths book) that started with the Schrodinger equation, wavefunctions, and then followed by approximation techniques. Somewhere in the middle of all of that, they awkwardly shoehorned Dirac notation and the mathematical postulates.
I was able to solve the problems, but I could never holistically wrap my mind around the structure theory. In other words, I could not articulate the reasons for why things were done in the way that they were. Turns out that starting out with wave mechanics is a terrible route. It is a special case of the more general theory, mainly convenient for calculating continuous quantities in a few practical models. But it does not teach intuition well! It is too easy to muddle in classical intuition when the curriculum presents this first. The real intuition comes from seeing how the constraints of probability under time evolution necessitate the use of complex vector spaces, eigenbasis, hermitian operators, etc. to elegantly calculate values. I found a helpful set of videos for anyone in a similar position. They have a fairly low view count for their quality, perhaps because they assume you already have some background:
https://www.youtube.com/c/ProfessorMdoesScience/videos
