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Published online by Cambridge University Press: 16 July 2025
This chapter builds the formal structure of quantum mechanics on the basis of five postulates. These postulates unify and formalize the concepts of matrix and wave mechanics introduced in Chapter 1. The first three postulates provide the framework for mathematical modelling of isolated systems and observables. The fourth postulate establishes relationship between theoretical description and experimental observations. Describing time evolution of a system is the content of the fifth postulate. The formalism is then extended to describe a composite system in terms of its constituent subsystems.
The formalism for describing a subsystem of a composite system, leading to the concept of density operator, is developed in Chapter 6.
Postulate 1: On Representing an Isolated System
An isolated system is described by a vector in the Hilbert space. The vectors differing only by a multiplying constant represent the same physical state.
A vector representing the state of a system is also referred to as a state vector. The implications of this postulate are
• The concept of the Hilbert space has been introduced in Chapter 2. Following the notation therein, the state of an isolated system according to the postulate in question is represented by a ket . A particular state is characterized by a label inside the ket. Thus, stands for a particular state of a given system.
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