Infinite square well — uncertainty principle

physics

Problem

For the nn-th stationary state of the infinite square well (width aa, with V=0V=0 for 0<x<a0<x<a and infinite walls), compute ⟨x⟩\langle x\rangle, ⟨x2⟩\langle x^2\rangle, ⟨p⟩\langle p\rangle, ⟨p2⟩\langle p^2\rangle, σx\sigma_x, and σp\sigma_p. Check that these are consistent with the Heisenberg uncertainty principle. Which state comes closest to the uncertainty limit?

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