Postulates of Quantum mechanics

Postulates of Quantum mechanics

While I was spending my quarantine time recalling my university studies, my mind fell deeply for an interesting and an easy topic that is the ‘postulates of quantum mechanics’. Perhaps, this topic shows us a path towards the basics of quantum mechanics.

 

Let’s discuss them in a very easy way…

There are basically four postulates of quantum mechanics, which are as under:

Postulate # 1:

                         For every physical observable, let say ‘a’, there is an associated mathematical operator ‘ Ậ ‘. The associated operator gives the only possible results of the measurements of observable.

Mathematically:

Ậ(f(x)) = g(x) ------    (1)

Where

·    Ậ is an operator.

·    f(x) is any functions/observable.

·    g(x) is a new function obtained because of the operator Ậ applied on the function f(x).

Example:

For sake of easiness, let the operator

 Ậ is d/dx  and the function f(x) = 2x

Equation (1) can be written as: 

(d/dx) 2x = 2

Here the operator  d/dx  applied on the function ‘2x’ and produced a new function ‘2’.

So, from the above discussion we can conclude that,

When an operator operates on any function, it changes the original function f(x) into a new function g(x). This can be seen mathematically from equation (1).

Ậ(f(x)) = g(x)

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Hopefully, this blog has helped you to understand the 1^st postulate of quantum mechanics. Your feedback in the comment section will be appreciated and responded on time.

We will discuss the further postulates in my next blog.