Quantum Math requirements of QM by J. J. Sakurai?

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To thoroughly understand J. J. Sakurai's "Modern Quantum Mechanics," a strong foundation in various mathematical disciplines is essential. Key areas of knowledge include calculus (up to third semester), differential equations (both ordinary and partial), linear algebra, vector calculus, and real analysis. Additionally, familiarity with algebra, group theory, operator theory, and representation theory enhances comprehension. While many physics majors complete standard coursework in these areas, a solid grasp of undergraduate quantum mechanics is considered the most crucial prerequisite for engaging with Sakurai's material. Overall, while extensive mathematical knowledge is beneficial, the emphasis should be on understanding the core concepts of quantum mechanics.
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What math should a person know to THOROUGHLY understand everything in this textbook(J. J Sakurai. Modern Quantum Mechanics)?

(For refrence)
cal2
cal3
diffeq1(ode)
diffeq2(pde)
linealg
vectorcalc
realanal1
realanal2
 
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To thoroughly understand absolutely everything with zero mathematical mystery in Sakurai's book you would need pretty much everything you listed, plus knowledge of algebra/groups, operator theory, and representation theory.

Most physics majors go through the standard three of four terms of calculus, have one or two linear algebra courses, learn about complex variables/DEs from mathematical physics courses, and then probably have a smattering of understanding of more advanced topics that they learned directly "from the physics", and we seem to get along with Sakurai once we get to grad school. Don't sweat the prerequisites for mathematics too much - the most important prerequisite for studying Sakurai is a year of undergrad QM.
 

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