Hello everyone today we will discuss Quantum chemistry Question and Answer for CSIR NET **GATE** IIT JAM and other entrance examinations as per. we have to talk about a few difficult questions asked in the previous year’s GATE 2018. we have to solve those questions with Proper calculation of physical chemistry way. Today we have to talk briefly to discuss and solve the question of the commutative operator in the Quantum chemistry chapter.

### What is a commutator operator?

The commutator operators like this [A, B]. Where A and B is a different type of operators that are commuted with each other if [A, B] =0. In the case of the commutator operators, not equal to zero ( [A, B] ≠0), the two operators do not commute two each other. Or two operators do not calculate simultaneously. Operators do not calculate at the same time.

#### Note:

If the commutator operator calculates simultaneously, two operators commute to each other. Otherwise, operators do not equal zero which means two operators do not commute, two operator does not calculate at the same time.

Problem-solve:

You can try to those problems solve in an easy way. If you have clear that the concept of operator applies in any function then you can solve it. The question has given below:

#### Q.1. Q.1. Consider the operator 𝒂_{+}= 𝟏/√𝟐(𝒙+𝒊𝒑_{𝒙}) and 𝒂_{−}= 𝟏/√𝟐(𝒙−𝒊𝒑_{𝒙}) where x and px are the position and linear momentum operators, respectively. The commutator [a_{+}, a_{–}] is equal to

_{+}= 𝟏/√𝟐(𝒙+𝒊𝒑

(A) 𝐢ℏ (B) −𝐢ℏ

(C) ℏ (D) -ℏ

##### Answer: Quantum chemistry Q.1

In this question given to operators a+ and a- above the question is commuted with function check. Find out the commutative operators in the 𝜓 function.

Finally, we have to solve this question very easily using the commutative operator. The important note is that [P_{x}, x] = -iћ Where P_{x} is the linear momentum and X is the position operator.

The final answer to the given questions commutators is ћ.

#### Book Reference:

Quantum chemistry book by Donald A McQuarrie is one of the most readable and popular books. For a chemical science entrance examination, aspirants must follow this book as a textbook.

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