Using your results for Problems P 18.11, 17, 29, and 32, calculate the uncertainties in the position and momentum 2 p = p 2

Using your results for Problems P 18.11, 17, 29, and 32, calculate the uncertainties in the position and momentum σ²_p = 〈p²〉 − 〈p〉² σ²_x = 〈x²〉 − 〈x〉² for the ground state (n = 0) and first two excited states (n = 1 and n = 2) of the quantum harmonic oscillator. Compare your results with the predictions of the Heisenberg uncertainty principle.