we have shroedinger's differential equation, heisenberg's matrix mechanics, dirac's formalism, and feynman sum over histories stuff. now i may be wrong and and i really don't know anything but i think that these are all equivalent and some even the same thing. but if im going to learn QM for keeps, which is the most useful formalism? i see the point in wasting time learning one and then relearning how to do the same thing a different way. i think i might as well learn the best and just use that. any dissenting opinions on my aforementioned opinion appreciated. thx.
Your laziness impresses me, but ice is right. Besides, you don't have to learn the same things over and over again. The methods are complimentary. Edit: I meant Dr Transport is right.
The thing is: sometimes one formalism is more natural than another, depending on the problem at hand. For example, in QFT, the Feynman approach is most often used, while in nonrelativistic QM, Schrodinger is useful when working in position/momentum space, while Heisenberg is useful when spin is involved... but even that rule of thumb is violated as often as it's true! Sorry, ice109 - there is no one good choice. The literature covers all of them, so if you want to understand papers, you need all the formalisms. But they're not all that hard! Once you learned the fundamentals, going from Schrodinger to Heisenberg, for example, is no trouble.
Well- I'm writing a paper at the moment where I use both Feynman path-integral and Schrodinger's equation to find particle momenta. I also solve S.E. using a matrix method, which connects with Heisenberg's formulation. Does that answer your question?
Perfectly said, look through a years worth of any journal and you will find all of the representations.