Mathematics of Quantum Mechanics

Agreegate
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I have a question about learning the mathematics of Quantum Physics...

So, I've been really interested in Astronomy and Quantum Physics since I was a kid. Owing to some accidental education and career choices, I however, ended up becoming a Business Consultant. Although I have spend most of my life reading about and learning about Quantum Mechanics, Physics and Astronomy, but now, I have reached a point where I understand most of the theories in principle, but lack any understanding of how they work mathematically... It feels synonymous to being an illiterate person who has to rely on what others read to him from a storybook, but cannot read it himself.

My basic mathematics knowledge is set very very far back at this point. I hardly remember high school mathematics, but can probably recall it again with some effort and learn more on top of it. What I need, is a guidance on what kind of mathematics I should invest my time in learning, so that I can work towards mathematically understanding Quantum Physics (no academic courses, I want to learn it in my own time, myself, since, I'm not aiming for an academic or professional career). Also, if someone can recommend a book or website, etc, which can guide me through basic to advanced mathematics of Quantum Physics, then that would be brilliant. Thanks for your help in advance...
 
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Agreegate said:
I have a question about learning the mathematics of Quantum Physics...

So, I've been really interested in Astronomy and Quantum Physics since I was a kid. Owing to some accidental education and career choices, I however, ended up becoming a Business Consultant. Although I have spend most of my life reading about and learning about Quantum Mechanics, Physics and Astronomy, but now, I have reached a point where I understand most of the theories in principle, but lack any understanding of how they work mathematically... It feels synonymous to being an illiterate person who has to rely on what others read to him from a storybook, but cannot read it himself.

My basic mathematics knowledge is set very very far back at this point. I hardly remember high school mathematics, but can probably recall it again with some effort and learn more on top of it. What I need, is a guidance on what kind of mathematics I should invest my time in learning, so that I can work towards mathematically understanding Quantum Physics (no academic courses, I want to learn it in my own time, myself, since, I'm not aiming for an academic or professional career). Also, if someone can recommend a book or website, etc, which can guide me through basic to advanced mathematics of Quantum Physics, then that would be brilliant. Thanks for your help in advance...
I hear good things about The Theoretical Minimum.
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
 
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Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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