The uncertainty product
Answer to Problem 30P
The uncertainty product
Explanation of Solution
To compute uncertainty in distance, first calculate average distance and average square distance using radial probability distance.
Write the expression for probability density.
Here,
Write the expression for average distance.
Here,
Substitute
Write the expression for Average Square of distance.
Here,
Substitute
Substitute
Substitute
Write the expression for uncertainty of radius.
Substitute
Write the expression for the average potential energy.
Write the expression for average momentum.
Here,
Substitute
From symmetry
So product of uncertainty in momentum and uncertainty in position is:
This value
Conclusion:
Thus, the uncertainty product
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Chapter 8 Solutions
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