Concept explainers
(a)
Interpretation:
The given wavefunction is to be normalized over the indicated range.
Concept introduction:
In
Answer to Problem 10.31E
The normalized wavefunction is
Explanation of Solution
The given wavefunction is
Assume the normalization constant of the wavefunction as
The normalization of given wavefunction is done by the formula,
Where,
•
•
Substitute the value of
Solve the above equation.
Only positive square root is taken for normalization constant. Therefore, the normalized wavefunction is
The normalized wavefunction is
(b)
Interpretation:
The given wavefunction is to be normalized over the indicated range.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 10.31E
The normalized wavefunction is
Explanation of Solution
The given wavefunction is
Assume the normalization constant of the wavefunction is
The normalization of given wavefunction is done by the formula,
Where,
•
•
Substitute the value of
Solve the above equation.
Only positive square root is taken for normalization constant. Therefore, the normalized wavefunction is
The normalized wavefunction is
(c)
Interpretation:
The given wavefunction is to be normalized over the indicated range.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 10.31E
The normalized wavefunction is
Explanation of Solution
The given wavefunction is
Assume the normalization constant of the wavefunction is
The normalization of given wavefunction is done by the formula,
Where,
•
•
Substitute the value of
Function
From Appendix 1,
From this relation, the above equation becomes,
Since
Only positive square root is taken for normalization constant. Therefore, the normalized wavefunction is
The normalized wavefunction is
(d)
Interpretation:
The given wavefunction is to be normalized over the indicated range.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 10.31E
The normalized wavefunction is
Explanation of Solution
The given wavefunction is
Assume the normalization constant of the wavefunction is
The normalization of given wavefunction is done by the formula,
Where,
•
•
Substitute the value of
Assume,
Substitute the value of
From Appendix 1,
From this relation, the above equation becomes,
Only positive square root is taken for normalization constant. Therefore, the normalized wavefunction is
The normalized wavefunction is
(e)
Interpretation:
The given wavefunction is to be normalized over the indicated range.
Concept introduction:
In quantum mechanics, the wavefunction is given by
Answer to Problem 10.31E
The normalized wavefunction is
Explanation of Solution
The given wavefunction is
Assume the normalization constant of the wavefunction is
The normalization of given wavefunction is done by the formula,
Where,
•
•
Substitute the value of
Assume,
Differentiate equation
Substitute value of
Substitute the value of
It is known that,
Using this relation, the above equation becomes,
From Appendix 1,
Using this relation, the above equation becomes,
Therefore, the normalized wavefunction is
The normalized wavefunction is
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Chapter 10 Solutions
Physical Chemistry
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