Concept explainers
(a)
The probability that the particle will be found in the region.
(a)
Answer to Problem 48P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The one-dimensional box regionis
The particle is in the ground state.
The given region is
Formula used:
The expression for probability for finding the particle in ground stateis given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probabilityis 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)
Answer to Problem 48P
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
(c)
The probability that the particle will be found in the region.
(c)
Answer to Problem 48P
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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