By Sunil Bhardwaj

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The relationship between quantum mechanics and operators has helped to present the concepts in the form of some postulates. These Postulates are:

1. The state of a system is described by a wave function $${ \Psi (x, y, z, t) }$$.

$$\widehat { A } \Psi = a\Psi$$

2. Every Observable physical property of a system can be characterised by a linear operator. e.g. Position (A) is characterised by operator $$\widehat { A }$$.

3. The possible value of any physical quantity of a system are given by Eigen value (a) in the operator equation.

4. When an operator $$\widehat { A }$$ is operated on a function $${ \Psi }$$, an average result obtained is given by,

$$\left< A \right> =\frac { \int _{ -\infty }^{ +\infty }{ { \Psi }^{ * }.A\Psi .d\tau } }{ \int _{ -\infty }^{ +\infty }{ { \Psi }^{ * }.\Psi .d\tau } }$$

5. As all the wave functions are time dependent. i.e. $${ \Psi (x, y, z, t) }$$ then its subsequent behaviour should be described by time-dependent Schrödinger equation. Which is,

$$-\frac { ih }{ 2\pi } .\frac { \partial \Psi \left( x, y, z, t \right) }{ d\tau } = \widehat { H } \Psi \left( x, y, z, t \right)$$

Where $$\widehat { H }$$ is known as Hamiltonian Operator of the system.

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