Basic Postulates of Quantum Mechanics


A postulate is a statement that is assumed to be true without proof, whereas a theorem is a true statement that can be proven. The essence of quantum postulates is represented in this with a set of seven postulates. These postulates provide a connection between the physical world and the mathematical framework of quantum mechanics.

Postulates of Quantum Mechanics:

The basic postulates of quantum mechanics are –

i. Every physical system has an associated complex vector space with an inner product (Hilbert space) known as the state space of the system. A unit vector represents the physical system in the state space, this unit vector known as the state vector contains all the information that can be known about the system.

ii. `All observables (measurable properties) of a physical system are represented by Hermitian operators acting in the system’s state space. Any measurement performed on a quantum system necessarily involves some interaction between the insured obtaining a certain outcome the eigenvector of the operator with eigenvalue.

iii. The probability of measuring an observable with eigenvalue in a quantum state is

where |a> is an eigenvector of the corresponding Hermitian operator with eigenvalue.

iv. Measurements in systems having the same state vector may not result in the same outcomes. Only the probabilities of various outcomes can be known.

v. The expectation value of a measurable quantity Q is defined as the average of values that is likely to be obtained if Q is measured on a large number of systems having the same state vector |u>. The expectation value is postulated to be


Provided <u|u>=1.

vi. The state space of a composite physical system is the tensor product of the state spaces of the component systems.

vii. The evolution of a quantum system in time is described by a unitary transformation.