The justification for postulates may be that quantum mechanics represented such a significant departure from the thinking in classical physics that it was necessary to make a clear statement of these differences. But, it is a bit of an odd procedure in science to state that something is a postulate. That is to say, one is not calling it a hypothesis per se. Rather it is a system of statements that are internally consistent and taken to be a representation of reality. In practice, the statements are treated as hypotheses, or have been. A the present time, the basic thinking the is the foundation of quantum mechanics is widely accepted. It has been an enormously successful branch of physics in that it can be used to explain molecular structure and properties (among other things), which are of great interest in Chemistry. In this section we consider the statements, known as postulates, and their implication.

Braket formalism (Dirac notation)

The use of integrals in quantum mechanics become quite cumbersome. There are many of them and they can be very complicated. Dirac proposed a notation that would simplify these complex integrals. It is known as braket notation where is a ket. Only a physicist would come up with with the nomenclature. Anyway, the braket represents the integral of x*y over all space. The wave function in the bra is in its complex conjugate form. You may also think of a braket as a dot product.