## Problem 10.3: Determine the expectation values for the energy eigenfunction

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A particle is in a one-dimensional box of length *L* = 1. The states shown are normalized. The results of the integrals that give <*x*> and <*x*^{2}> and <*p*> and <*p*^{2}>. You may vary *n* from 1 to 10. Restart.

- What do you notice about the values of <
*x*> and <*x*^{2}> as you vary*n*? - What do you think <
*x*^{2}> should become in the limit of*n*→ ∞? Why? - What do you notice about the values of <
*p*> and <*p*^{2}> as you vary*n*? - For
*n*= 1, what are Δ*x*and Δ*p*?

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