An unconventional approach would be to study quantum computation or quantum information theory first.
What is 'unusual' about quantum mechanics is the mathematical underpinnings, which is essentially a generalization of probability theory. (I have heard more than one colleague say that quantum mechanics is simply physics which involves 'non-commutative probability', i.e. in testing whether some collection of events are realized for some sample space, there is a pertinent sense of the order in which one tests those events.) To the extent that this is true, it is not important to be learning the actual physics alongside that mathematical underpinning, so long as you can learn about something evolving e.g. under the Schrödinger equation or collapsing under measurement.
Studying quantum information evolving under a computational process is one way you could achieve that. Because the narrative of the field is less about the crisis in physics in the 20s–40s, and more about physicists and computer scientists struggling to find a common language, the development is clearer and there is a better record of justifying the elements of the formalism from a fundamental standpoint. By studying quantum information and/or quantum computation, you will be able to decouple the learning of the underpinnings from the learning of the physics, and thereby get to the heart of any conceptual troubles you may have; and it will give you a tidier sandbox in which to play with ideas.
To this end, I recommend "Nielsen & Chuang", which is the standard introductory text of the field. It's suitable as an introduction both for those coming from a computer science background, and from a quantum physics background; so apart from learning some of the formalism, you can get some exposure to some of the physics as well. There are other texts which I have not read, though; and about a bazillion pages of lecture notes floating around on the web.
This post imported from StackExchange Physics at 2014-03-22 16:59 (UCT), posted by SE-user Niel de Beaudrap