Question 4 A one-dimensional harmonic oscillator has energy eigenfunctions un(x) with n = 0, 1, 2, ... The momentum oper

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Question 4 A One Dimensional Harmonic Oscillator Has Energy Eigenfunctions Un X With N 0 1 2 The Momentum Oper 1 (65.82 KiB) Viewed 27 times

Question 4 A one-dimensional harmonic oscillator has energy eigenfunctions un(x) with n = 0, 1, 2, ... The momentum operator, P can be expressed as P₂ = √2/₁ (—ù), - where the lowering operator is A and the raising operator is ¹. (a) By using the properties of the lowering and raising operators, A (or otherwise) show that (px) = 0 in the state 4(x). and A¹ (b) Given that ħ² P2² ·(¹ + ¹ —  — ¹¹), 2a² where a is a constant, calculate (p²) in the state ₁(x). =