부산대학교 도서관

This chapter begins with basic complex numbers, including their polar form and their representation with Argand diagrams. This leads naturally into a discussion of the phase of a complex number, and the roles of overall and relative phases. All this paves the way for consideration of the complex nature of quantum states. It is shown how, even for spin 1/2 systems, complex coefficients are required to represent adequately states, and the coefficients' phases play a crucial role. Changes in coefficients' phases — which can be brought about by a unitary operator — can alter probabilities, and the conditions under which this occurs are discussed. An example from spin 1/2 illustrates. Finally, the preceding ideas are discussed in the context of wavefunctions.