Concept explainers
The uncertainty product
Answer to Problem 11P
The uncertainty product
Explanation of Solution
Formula used:
The expression for ground state of harmonic motion is given by,
The wave function for ground state is,
Calculation:
The expression for ground state of harmonic motion is calculated as,
Let,
Then,
For the limits,
The expectation value for
For the limits,
By definition of Gamma function,
Then,
The uncertainty in position is calculated as,
Further simplify the above,
The uncertainty in momentum is calculated as,
Further simplify the above,
Multiply equation (1) and (2).
Conclusion:
Therefore, the product
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Chapter 35 Solutions
Physics for Scientists and Engineers, Vol. 3
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