postulates of Quantum mechanics (2 and 3)

In our previous meeting we discussed the postulate # 1 of Quantum mechanics, In this blog we will further our understanding about postulate # 2 and postulate # 3.

Postulate # 2

              Statement: 

                                       Allowed values of the measurements of observable “a” are given by eigenvalues of operator “A” associated with the observable.

Explanation:

                         When an operator is applied on any observable and if it gives back the same observable times a constant, then the constant will be called the value of the observable.

The constant is also called the eigenvalue of the equation. And the equation as a whole is called eigenvalue equation.

Mathematically:

                            Ậ (f(x)) = c f(x)  ------------- (2)

Where

          Ậ is any operator

          f(x)  is any function

          c is a constant, this is called eigenvalue.

we see in equation (2) that we are getting the same original function f(x) even after applying the operator on L.H.S of the equation. we are getting a constant as an additional term.

 Equation (2) is called the eigenvalue equation as it contains the eigenvalue of the observable.

Postulate 3: 

                  Statement:

                              For every system, there exists a state function “ᴪ” that contains all the information about the system.

Facts about ᴪ:

 The symbol ᴪ has impressed me when I was enrolled as an undergraduate student . here are few important point which are obligatory , (I should say), to know, these are

     ·     ᴪ is called the wave function.

·     ᴪ is a function of spatial coordinates

·       ᴪ can be a complex number.

_ __  _  ___ ___ __ _

Your feedback and question will be appreciated.