(4a³ 1/4 T xe-ax²/2, where a = μω ħ The harmonic oscillator eigenfunction ₁(x) = (a) Find (x²) for an oscillator in this state, and express your result in terms of µ, w, and ħ. 1 (b) In an eigenstate it is always true that (T) = (V) for a harmonic oscillator. If ↑ = -p² 2μ and ŷ = ½µw²î², find (p²) when the system is in the state ₁ (x). (Note: You can use 2 the result found in part (a), or compute it directly from the form of the operator p.)

(4a³ 1/4 T xe-ax²/2, where a = μω ħ The harmonic oscillator eigenfunction ₁(x) = (a) Find (x²) for an oscillator in this state, and express your result in terms of µ, w, and ħ. 1 (b) In an eigenstate it is always true that (T) = (V) for a harmonic oscillator. If ↑ = -p² 2μ and ŷ = ½µw²î², find (p²) when the system is in the state ₁ (x). (Note: You can use 2 the result found in part (a), or compute it directly from the form of the operator p.)