Harmonic oscillator via ladder operators

physics

Problem

Find ⟨x⟩\langle x\rangle, ⟨p⟩\langle p\rangle, ⟨x2⟩\langle x^2\rangle, ⟨p2⟩\langle p^2\rangle, and ⟨T⟩\langle T\rangle (the average kinetic energy) for the nn-th stationary state of the harmonic oscillator, using the ladder-operator (creation/annihilation) method. Check that the uncertainty principle is satisfied.

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