# Basic Postulates of Quantum Mechanics

## Postulate:

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

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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
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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.