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a)

Compute the exact expectations , <r> and for the ground state of hydrogen. In our uncertainty principle analysis, we assumed that these were given approximately by , and , respectively, where . Now that you know the exact correct results, what was the greatest factor by which we were in error in making this assumption?

Math hint: You may find the second line of the math hint for problem 1 useful in doing this problem as well.



Prof. Tomas Alberto Arias
Thu Oct 12 17:30:59 EDT 1995