A one-dimensional harmonic oscillator has energy eigenfunctions un(a) with n = 0, 1, 2,... The momentum operator, p, can

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A One Dimensional Harmonic Oscillator Has Energy Eigenfunctions Un A With N 0 1 2 The Momentum Operator P Can 1 (25.24 KiB) Viewed 20 times

A one-dimensional harmonic oscillator has energy eigenfunctions un(a) with n = 0, 1, 2,... The momentum operator, p, can be expressed as Pr ·(Â-¹), A √2a where the lowering operator is  and the raising operator is ¹. (a) By using the properties of the lowering and raising operators, A and A¹ (or otherwise) show that (p₂) = 0 in the state (7). (b) Given that h² · 2º² (¹ + ¹ —  – ¹¹'), - where a is a constant, calculate (p2) in the state (r).