I have recently acquired a highly advanced book in quantum mechanics which I am determined to master, however a lot of the mathematics is unfamiliar to me so could someone tell me the knowledge of mathematics (i.e the topics) I would need to understand before I can attempt to grasp such a complex subject?
- 1 decade agoBest Answer
-linear algebra: complex numbers, eigenvectors, eigenvalues
-functional analysis: Hilbert spaces, linear operators, spectral theory
-differential equations: partial differential equations, separation of variables, ordinary differential equations, Sturm-Liouville theory, eigenfunctions
-harmonic analysis: Fourier transforms
Undergrad math is not enough, you will need to study some advanced math like Hilbert spaces. I suggest you start with fundamental QM books because some of them will cover the math required.
- Sidereal HandLv 51 decade ago
It is possible to explain QM with little more than Algebra under your belt. However, that understanding doesn't come til you master Diff Eq's. I would suggest starting with a mental exercise, like explaining how Law of Conservation and Uncertainty account for material manifestations. No matter how advanced that sounds, any explanation will lead to further understanding. Then, try applying that knowledge to patterns of fields, such as the Quantum plane. If you're still with me, developing a mathematical formula for your observations will increase your understanding 100 fold.
- 1 decade ago
Basically the entire foundation of quantum mechanics is founded in what is called 'Hilbert space.' All assumptions about the nature of particle and wave interactions are contained within the definition of Hilbert space. The fundamental idea is that Hilbert space is composed of an infinite number of orthogonal dimensions and or coordinate axes.
You'll have to be familiar with probability theory and eventually more advanced statistical mechanics. You'll need a ton of differential equations, especially relating to separation of variables in the early aspects of QM. Matrix algebra, linear algebra, complex analysis, tons of fourier analysis, and an understanding of eigenvectors and eigenvalues.
You should review legendre's differential equation and legendre's associated differential equation, and bessel functions, as they show up early on.
- kennykLv 41 decade ago
calculus, vector calculus, linear algebra, complex analysis, differential equations
Most college level quantum mechanics books expect that you have had 3 semesters of college level calculus, 1 semester of differential equations, 1 semester of linear algebra, and some exposure to complex analysis. They also expect that you are familiar with classical mechanics and electrodynamics.
If you are really determined to learn quantum mechanics I would suggest starting with a modern physics textbook rather than a pure quantum mechanics text such as Griffiths. It will guide you through a less rigorous semi-classical approach.
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- thodeLv 43 years ago
hi Nuff; i for my area experience, with extremely no scientific evidence, that each and every decision we make daily provides an probability for yet another ( or parallel universe). I enroll in the Robert A. Heinlein concept, in all probability earlier a while yet, a brilliant fiction author. try "The form of The Beast" or "Stranger In a wierd Land"good easy enjoyable reads. yet time is a intense subject, and one i'm afraid I even have very fastened notions upon. As i think God created it,and holds it till, as you should declare the time is powerful, and guy would desire to circulate forward purely, living each and every 2nd to the fullest, as there is not any going decrease back. "The previous is historic past, the destiny a secret, we are able to purely stay interior the now." yet to punch a hollow into yet another universe, will in all probability take place sooner or later, what happens next? nicely which would be an entire distinctive universe lower back. LOL have enjoyable with this one! Bob
- Anonymous1 decade ago
to get more of an idea what you have to know, and a little bit of that knowledge thown in try
"Road to Reality" by Roger Penrose.
Starts with the basics and works up from there but still a brutal read!
- Anonymous1 decade ago
Algebra and calculus at a minimum.
- muddypuppyukLv 51 decade ago
I would start here........
- 1 decade ago
Try this link
you'll find what you seek.