What math and physics do I need to learn before studying quantum mechanics?

[Dmlac]

edit: I found what I was looking for. But Idk how delete the post

TL;DR: How much math and physics do I need to learn before I can understand quantum mechanics mathematically, especially equations like the Schrödinger equation?

What level of physics and mathematics do I need to reach before I can start understanding the mathematical side of quantum mechanics? For example, how deeply do I need to study calculus, classical physics, modern physics, etc? I can understand the concepts behind the equations and what they mean, but I'm not sure how much mathematical and physical knowledge I need to understand more complex equations in quantum mechanics.
I hope my question is clear. English isn't my first language.

 

[MidgetDwarf]

You will need functional analysis and everything that comes before.

Great news, is if you are okay with handwaving some of the math details, then knowledge of Vector Calculus, Linear Algebra, and some complex analysis can allow you to work through a book like Griffiths.

With just calculus, you learn what they call modern physics in the states (i call it intro to some topics of QM light)

 

[Dmlac]

You will need functional analysis and everything that comes before.

Great news, is if you are okay with handwaving some of the math details, then knowledge of Vector Calculus, Linear Algebra, and some complex analysis can allow you to work through a book like Griffiths.

With just calculus, you learn what they call modern physics in the states (i call it intro to some topics of QM light)

Thanks for the response. This really helped me figure out what I should study next. Luckily, I have access to Griffiths, so I will give it a try.

 

[MidgetDwarf]

i forgot to mention ODE. PDE are also good to know, but you can get a lot of milage just knowing ODE.

 

[bhobba]

The basics of calculus, such as those found in my favourite introductory book (can be studied after US Algebra 2 or Australian Year 9 math):
https://www.amazon.com.au/Quick-Calculus-Self-teaching-Manual-Self-instruction/dp/0471827223

Then:


To go further, you need more math. I recommend Boaz (surprisingly, having studied the book myself, you only need Quick Calculus as a prerequisite):

https://www.amazon.com.au/Mathematical-Methods-Physical-Sciences-3E/dp/0471198269

Then for a deep treatment, a text well respected on this forum, Ballentine:
https://www.amazon.com.au/Quantum-Mechanics-Leslie-Ballentine/dp/9810241054

Thanks
Bill

 

[Matterwave]

Then for a deep treatment, a text well respected on this forum, Ballentine:
https://www.amazon.com.au/Quantum-Mechanics-Leslie-Ballentine/dp/9810241054

Note that this is a rather advanced QM book aimed more towards advanced undergrads and grad students. It throws you into the deep end (Hilbert space completeness, the spectral theorem, Gelfand Triples) immediately. Might want to start with an easier book.

 

[bhobba]

Without a doubt, it should not be studied until you have completed the suggested reading list, especially Townsend's A Modern Approach to Quantum Mechanics and Boaz. Also strongly recommended to come to grips with Rigged Hilbert Spaces, Gelfand Triples, etc is a good book that introduces Distribution Theory (also a much better approach to Fourier Transforms and Series than Boaz), such as my favourite (which IMHO should be on the bookshelf of all mathematicians and physicists):
https://www.amazon.com.au/Theory-Distributions-Nontechnical-Introduction/dp/0521558905

Some readers may prefer to study Sakurai before Ballentine, considering the ebook is dirt cheap:
https://www.amazon.com.au/Modern-Quantum-Mechanics-J-Sakurai-ebook/dp/B0FJ7LK8PF

Thanks
Bill