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3. Let's have another swing at the one-dimensional harmonic oscillator. Suppose that
the oscillator is prepared in one of the eigenstates of the Hamiltonian, [½) = |n),
where ne {0, 1, 2, . . . }.
(c) Verify the validity of the Heisenberg uncertainty relation by evaluating the
(d) For which n is the Heisenberg uncertainty minimized, i.e. ^q^p = ħ/2?

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