There are lots of equivalent representations of the same thing, and for non relativistic QM i is by far the simplest way of proceeding. Part of learning QM is l

There are lots of equivalent representations of the same thing, and for non relativistic QM i is by far the simplest way of proceeding. Part of learning QM is learning that changing how you view the world without actually changing the world is a very powerful thing and sometimes more complex ways of thinking are actually easier "later on". A simple example is the equivalence of two complex parameters, alpha and beta, arranged in a 2-matrix and a real 3-matrix for the representation of rotation. Another example would be ladder operators for the simple harmonic oscillator -- arguably overcomplicated for the problem at hand, they form the basis of much of what follow (i.e. vacuum creation and annihilation operators). The whole point of the notational soup that one finds e.g. in an extended field theory is that it correctly generates a lot of these details "automatically". It's obtuse and makes doing simple things hard, but makes showing non-trivial relationships that are true in general very much easier than the alternative ;-).