A one-dimensional harmonic oscillator has energy eigenfunctions (x) with n = 0, 1, 2,... The momentum operator, P, can b

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A One Dimensional Harmonic Oscillator Has Energy Eigenfunctions X With N 0 1 2 The Momentum Operator P Can B 1 (51.74 KiB) Viewed 22 times

A one-dimensional harmonic oscillator has energy eigenfunctions (x) with n = 0, 1, 2,... The momentum operator, P, can be expressed as -i ℗₂ = √ (—ù), where the lowering operator is  and the raising operator is ¹. (a) By using the properties of the lowering and raising operators,  and A¹ (or otherwise) show that (pr) = 0 in the state 4(x). (b) Given that ħ² ¡ (¹ + ¹ —  — ¹¹), 2a² where a is a constant, calculate (p2) in the state 4(x).