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Concept explainers
(a)
The probability that the particle will be found in the region.
(a)
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Answer to Problem 49P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The one-dimensional box region is
The particle is in the first excited state.
The given region is
Formula used:
The expression for probability for finding the particle in first excited state is given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probability is calculated as,
Solving further as,
Conclusion:
Therefore, the probability that the particle will be found in the region is
(b)
The probability that the particle will be found in the region.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 49P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The given region is
Formula used:
The expression for probability for finding the particle in first excited state is given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probability is calculated as,
Solving further as,
Conclusion:
Therefore, the probability that the particle will be found in the region is
(c)
The probability that the particle will be found in the region.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 49P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The given region is
Formula used:
The expression for probability for finding the particle in ground state is given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probability is calculated as,
Solving further as,
Conclusion:
Therefore, the probability that the particle will be found in the region is
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Chapter 34 Solutions
Physics for Scientists and Engineers
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