
Concept explainers
(a)
Interpretation:
The value of
Concept introduction:
The importance of
(a)

Answer to Problem 7F.9P
The value of
Explanation of Solution
The value of
Multiply the parentheses as shown below.
Hence, the value of
(b)
Interpretation:
The value of
Concept introduction:
The importance of angular momentum is comparable to the linear momentum in translational motion. In quantum mechanics, commutator of two operators tells the measurement of two operators at a same time. The commutator of angular momentum in two different axes is calculated by the formula shown below.
(b)

Answer to Problem 7F.9P
The value of
Explanation of Solution
The value of
Multiply the parentheses as shown below.
Hence, the value of
(c)
Interpretation:
The value of
Concept introduction:
The importance of angular momentum is comparable to the linear momentum in translational motion. In quantum mechanics, commutator of two operators tells the measurement of two operators at a same time. The commutator of angular momentum in two different axes is calculated by the formula shown below.
(c)

Answer to Problem 7F.9P
It has been proved that the value of
Explanation of Solution
The value of
Further solve the above equation, by multiplying and dividing by
Hence, it has been proved that the value of
(d)
Interpretation:
The cyclic permutation order for linear momentum operators has to be proved.
Concept introduction:
The importance of angular momentum is comparable to the linear momentum in translational motion. In quantum mechanics, commutator of two operators tells the measurement of two operators at a same time. The commutator of angular momentum in two different axes is calculated by the formula shown below.
(d)

Answer to Problem 7F.9P
It has been proved that linear momentum operators follow the cyclic permutation order.
Explanation of Solution
The
The
The
From equation (1), it is clear that the
(e)
Interpretation:
The commutations of other two angular momentum operators, by following the cyclic order permutation have to be predicted.
Concept introduction:
The importance of angular momentum is comparable to the linear momentum in translational motion. In quantum mechanics, commutator of two operators tells the measurement of two operators at a same time. The commutator of angular momentum in two different axes is calculated by the formula shown below.
(e)

Answer to Problem 7F.9P
The value of the commutation of
The value of the commutation of
Explanation of Solution
The value of the commutation of
By following the cyclic order permutation, the value of the commutation of
Similarly, the value of the commutation of
This proves that the commutations of other two angular momentum operators follow cyclic permutation order.
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Chapter 7 Solutions
Atkins' Physical Chemistry
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