Hello Aspirant,

I hope you are doing well.

In order to study elementary quantum mechanics you must ideally have an understanding of the following mathematical ideas: Complex numbers. Partial and Ordinary differential equations. Integral calculus I-III.

Firstly, start by learning basic physics (Newtonian mechanics, electromagnetism, etc.),before learning quantum mechanics. Then, some mathematics like calculus I-III [single and multivariable with differentiation and integration], differential equations [ODEs], linear algebra and Fourier analysis.

Some resources:

• Wikipedia
• MIT Open CourseWare (OCW) http://ocw.mit.edu/courses/find-by-topic/
• Use an online textbook (or an actual tangible one, if you can), like this one (for an intro): http://www.physics.umd.edu/courses/Phys270/Jenkins/Griffiths_EPR_BellInequality_Excerpt.pdf
• http://www.youtube.com/playlist?list=PL701CD168D02FF56F & here: http://www.youtube.com/playlist?list=PL84C10A9CB1D13841

I hope this helps.

Good Luck

Hi,

Hope you are doing well!

Some important topic to study before quantam mechanics are:

• You should learn solution of Linear second order ODEs with constant coefficients,Special functions : Associated Legendre functions, Laguerre polynomials, Hermite polynomials,series solution method etc.
• You can study notion of linear vector spaces, linear transforms between vector spaces, linear functionals, basic and dimension of vector spaces from linear Algebra,Fourier transformation.
• In order to know the connection between classical and quantum mechanics you can have an idea on Hamiltonian formalism of classical mechanics and the Poisson bracket structure.
• You should study separation of variables,  Helmholtz equation, general solution construction of PDEs.
• You can also study old quantum theory and Energy quantization.

Hope it helps.

All the best for your future.