Re: I want to study Quantum Mechanics

     I’m not sure where to begin because I don’t know how much you already 
know about quantum mechanics, so I’ll take the safe way out and start at 
the beginning.  Quantum mechanics started at the beginning of the 1900s 
when physicists noticed matter had certain properties that classical 
physics (also known as Newtonian Physics) couldn’t explain – or at least 
couldn’t explain properly. 
     Basically, classical physics says that for any object, all energy 
levels are possible.  That is, an object can have any arbitrary amount of 
energy.  But when physicists started to experiment with atomic spectra, 
they noticed that the spectra were not continuous as classical physics 
predicted but rather the spectra seemed to be discontinuous, and only 
certain wavelengths were possible.  Max Plank (using blackbody radiation) 
was one of the first to notice this and propose an explanation.  According 
to Plank, energy could only exist in small packets, which he called quanta 
(hence the name quantum mechanics).
     Further experiments showed that matter had wavelike properties.  On 
the macroscopic scale, we cannot notice these properties, but on the 
microscopic scale, such as the scale of an atom, properties like 
wavelength and frequency are quite noticeable.  So now that we know matter 
has wavelike character, we have to find a way to incorporate that into our 
theory of the atom.  In the 1920s an Austrian Physicist named Erwin 
Scrodinger came up with the “Schrodinger Equation” and something he called 
the “wavefunction.”  According to these ideas, one cannot know exactly 
where a particle is, but we can speak of its location in terms of 
probability by using its wavefunction.
     Like Newton’s Laws of Motion, the Schrodinger Equation cannot be 
derived, but if one studies it closely, the equation can be used to derive 
other known and accepted relations such as the de Broglie equation, which 
relates an object’s momentum to it’s wavelength.
     Some other physicists who have contributed to quantum mechanics 
include Albert Einstein, Max Born, and Heisenberg (I’m not sure what his 
first name is).  Heisenberg probably demonstrated one of the most 
interesting ideas put forth by quantum mechanics.  According to the 
Heisenberg Uncertainty Principle, one cannot know an object’s momentum and 
location with arbitrary precision.  That is, if you know exactly how fast 
something is moving (you can use velocity to find momentum) then you 
cannot know exactly where that object is.
     As for what to study while in college:  You can either study physics 
or chemistry as an undergraduate.  In both majors you will get a taste of 
quantum mechanics.  Chemists usually deal with lower energy measurements 
and calculations since they are only interested in the relatively low 
energies involved in chemical reactions and to excite electrons in.  
Physicists are usually involved in the high-energy end of the spectrum 
when it comes to studying quantum mechanics.  If you major in chemistry 
you will probably get a small taste of quantum mechanics during your 
freshman year.  More advanced quantum mechanics is usually taught in 
junior or senior level physical chemistry course.  I’m not sure how it 
works out in if you were to major in physics; I’m sure depending on school 
it will vary.
     I’m not sure what the leading schools are for studies in quantum 
mechanics.  What’s really important is to go to a school that you like.  
Also remember that as an undergraduate you’ll study a wide variety of 
topics in your field, not just quantum mechanics.  As a graduate student, 
you will usually focus attention on one topic (such as quantum mechanics).
If you want to teach yourself some quantum mechanics basics any 
introductory text will probably do the trick.  Quantum mechanics also 
involves quite a bit of calculus, so a good math background will help 
quite a bit.  In fact, in order to understand a lot of quantum mechanical 
proofs and concepts, you will need to know how to differentiate and 
integrate equations as well as some basic formulas (some important 
formulas include Euler’s Formula and de Moivre’s Formula).
     Hope this helps!  Good luck with reaching your goal!