Of the specialized concepts and mathematical functions that crop up inĮlementary QM (e.g. Ordinary differential equations Basic probability and statistics A lot Representation and manipulation of complex numbers in terms of complexĮxponential functions, and the representation of waves using the same)ĭifferential and integral calculus of a single variable, including Linear algebra (mainly vector algebra and matrix algebra, andĮspecially including eigenvectors and eigenvalues, which areĪbsolutely central to QM) Complex numbers (especially the You can tackle basic, nonrelativistic QM at an introductory level with

This answer is Steve Denton's suggestion on Quora website. I come from a non-physics background and I have to learn quantum mechanics for my future studies and unfortunately I couldn't find any thorough answer on stackex unlike Steve Denton's in here With one linear algebra course and Calc I, CalcII, and CalcIII. The earlier edition of David Park is more standard and easy enough and can be understood I suggest using Dirac's book on QM! It uses very little maths, and a lot of physical insight. An ordinary Calculus II course covers ODE basics like separation of variables and stuff. Singular point, so most QM teachers re-do the special case of that theory needed for the hydrogen atom anyway, sadly but wisely assuming that their students never learned it. It would be nice if you had taken a course in ODE but the truth is, most ODE courses these days don't do the only topic you need in QM, which is the Frobenius theory for eq.s with a regular QM seems to use functional analysis, i.e., infinite dimensional linear algebra, but the truth is that you will do just fine if you understand the basic finite dimensional linear algebra in the usual linear algebra course and then pretend it is all true for Hilbert Spaces, too. You need linear algebra, but sometimes it is reviewed in the book itself or an appendix.

You don't need any probability: the probability used in QM is so basic that you pick it up just from common sense.

Griffiths intro to quantum mechanics