Concept explainers
(a)
To shows: That the wave function
(a)
Explanation of Solution
Any function is a solution of linear wave equation in general if it satisfies the equation completely.
The linear wave equation in general is,
The given wave function is,
Differentiate equation (I) partially with respect to
Again differentiate partially with respect to
Differentiate equation (I) partially with respect to
Again differentiate partially with respect to
Conclusion:
Therefore, the wave function
(b)
To shows: That the wave function
(b)
Answer to Problem 16.44P
The functional form of
Explanation of Solution
It can be proved as,
Therefore,
The functional form of
The functional form of
Conclusion:
Therefore, the functional form of
(c)
Repeat part (a) and part (b) for the function
(c)
Explanation of Solution
Any function is a solution of linear wave equation in general if it satisfies the equation completely.
The given wave function is,
Differentiate equation (I) partially with respect to
Again differentiate partially with respect to
Differentiate equation (I) partially with respect to
Again differentiate partially with respect to
From the trigonometry,
Add equation (I) and (II).
Conclusion:
Therefore, the functional form of
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Chapter 16 Solutions
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