Concept explainers
(a)
The sketch of the real part of the matter wave pulse shape
(a)
Answer to Problem 35P
The real part of the matter wave pulse shape
Explanation of Solution
Write the expression for the matter wave pulse shape.
Here,
Write the expression for
Here,
Put the above equation in equation (I).
Simplify the above equation.
Take
Take the derivative of
Put the above two equations in equation (II).
Write the real part of
Here,
The plot of
Conclusion:
Therefore, the real part of the matter wave pulse shape
(b)
To show that the width of the matter wave pulse is
(b)
Answer to Problem 35P
It is showed that width of the matter wave pulse is
Explanation of Solution
Write the standard form of the Gaussian function with width
Comparison of equation (III) with the above expression shows that
Conclusion:
Therefore, it is showed that width of the matter wave pulse is
(c)
The width
(c)
Answer to Problem 35P
The width
Explanation of Solution
Compare equations (III) and (IV) to write the expression for
Rewrite the above equation for
Use equations (V) and (VI) to find the value of
Conclusion:
Thus, the width
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Chapter 5 Solutions
Modern Physics
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