I What Mathematical Theories Are Essential for Understanding Quantum Physics?

Michel Raskin
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Besides the basics what are the theories in math that I need to know for learning quantum physics?
And what books do you recommend for learning then?
 
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I suggest a forum search. Your question has been answered here several times. A good place to start is often the links provided at the end of this page (these are bot-generated, so may not be as applicable as you would like but still ... a good place to start).
 
You basically need linear algebra and calculus. A good grasp of complex algebra is also necessary.
 
J. J. Sakurai, Modern Quantum Mechanics
 
Alright thank you all I will look up
 
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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