- Question 4 A One Dimensional Harmonic Oscillator Has Energy Eigenfunctions Un X With N 0 1 2 The Momentum Oper 1 (46.89 KiB) Viewed 134 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 -i P₁ = ( – ¹), √2a where the lowering operator is A and the raising operator is ¹. (a) By using the properties of the lowering and raising operators, A and A¹ (or otherwise) show that (p.) = 0 in the state 4(x). (b) Given that ħ² Pr (¹ + ¹ —  — ¹¹), = 2a² where a is a constant, calculate (p2) in the state 4(x). [2] [3]