
Concept explainers
(a)
Interpretation:
The average value of position,
Concept introduction:
In

Answer to Problem 10.63E
The average value of position,
Explanation of Solution
The given wavefunction is
The normalization constant of the given wavefunction is assumed to be
The normalization of given wavefunction is done by the formula,
Substitute the value of
Solve the above equation.
Only positive square roots are taken for normalization constant. Therefore, the normalized wavefunction is
The position operator is defined as
The average value of
Where,
•
•
Substitute the value of
Solve the above expression for the value of
Therefore, the average value of position,
The average value of position,
(b)
Interpretation:
The average value of position,
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 10.63E
The average value of position,
Explanation of Solution
The given wavefunction is
The normalization constant of the given wavefunction is assumed to be
The normalization of given wavefunction is done by the formula,
Substitute the value of
Solve the above equation.
Only positive square root is taken for normalization constant. Therefore, the normalized wavefunction is
The position operator is defined as
The average value of
Where,
•
•
Substitute the value of
Solve the above expression for the value of
Therefore, the average value of position,
The average value of position,
(c)
Interpretation:
The average value of position,
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 10.63E
The average value of position,
Explanation of Solution
The given wavefunction is
The normalization constant of the given wavefunction is assumed to be
From Appendix
The normalization of given wavefunction is done by the formula,
Substitute the value of
Assume
Substitute the value of
Solve the above equation.
Only positive square root is taken for normalization constant. Therefore, the normalized wavefunction is
From Appendix
The average value of
Where,
•
•
Substitute the value of
Assume
Substitute the value of
Therefore, the average value of position,
The average value of position,
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Chapter 10 Solutions
Physical Chemistry
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