(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.)
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Transcribed Image Text:The harmonic oscillator eigenfunction ₁(x) =
=
4a³\1/4
e-ax²/2, where a = μω
ħ
(a) Find (x²) for an oscillator in this state, and express your result in terms of u, w, and ħ.
1
(b) In an eigenstate it is always true that (T) = (V) for a harmonic oscillator. If ↑
=-=-=-=A²
2μ
1
and ✩ = µw²x², find (p²) when the system is in the state 1₁ (x). (Note: You can use
the result found in part (a), or compute it directly from the form of the operator p.)
2
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