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Learning quantum mechanics at age 14
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If you want to learn about quantum physics and really understand you
need to learn first how to do calculations with vectors and matrices.
Look in your local library for math books, about 'linear algebra' or
'analytic geometry'. You may have to try several before you find one
suitable at your level. (wikipedia may also help to explain concepts
you don't know yet.)
Linear algebra (i.e., vectors and matrices) is more fundamental
to quantum mechanics than calculus, although the latter is needed
to understand how things change steadily with time.
But one can understand the time-independent part of quantum mechanics
already without calculus, namely everything involving entanglement,
Schroedinger's cat, quantum cryptography, and the like.
This only needs linear algebra, which may be easier. (On the other hand,
calculus is not really difficult either, once one gets used to it.)
Maybe at first it is better to get math schoolbooks from your
older peers. Good school books are written in a way that they can be
used for self study. If you are motivated it can be very exciting!
You can also look at what comes after school - at
http://tutorial.math.lamar.edu/
you find an online course giving you a full background in what you need
in order to master quantum mechanics. And you'll see what school stuff
you need to learn first - namely everything you do not understand when
reading the first pages of the lecture notes.
If you like math, learning in advance is much less work than you might
think, and it is fun! Just start with next years textbook and read it
in your spare time! I started reading math beyond my age when I was 12,
and never regretted it.
With the right motivation, you can learn 10 times as fast
as when you just wait till the subject comes up in school!
And it will be 10 times as interesting!
You don't need to do all the exercises but just enough that you
think you know how it works. Go back to practicing more if you
need it. This speeds up things a lot. You'll need a lot of practice,
but you'd practice on the things that currently interest you, and
that you perceive as a barrier for further understanding.
Also, you don't need to read everything in the order it is in
the book - just go where your curiosity leads you, and if you
encounter something you don't know yet, go back to where it was
introduced. In this way you get the idea of what is happening
long before you understand it thoroughly, and it will be a
motivation to learn the missing things.
Learning math and physics is a life-long challenge (so much interesting
stuff accumulated over the centuries...), and you can't start early
enough.
At any time in life there will be some parts you understand well, some
parts you understand partly or superficially only, and some parts
where you know little more than a few buzz words. Only the boundaries
between these areas move as you get more experienced. So you need
not aim at fully understanding everything on first acquaintance,
but learn whatever you can in whatever order you pick it up.
The stuff to be practiced and learnt well is that part that comes up
over and over again. When you realize that something belongs to this
category then you know what to learn and practice consciously.
And because you know why you need it, you'll be much quicker in seeing
how to do it!