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

[answerhappygod]

A One Dimensional Harmonic Oscillator Has Energy Eigenfunctions Un X With N 0 1 2 The Momentum Operator P Can 1 (79.68 KiB) Viewed 21 times

A one-dimensional harmonic oscillator has energy eigenfunctions un(x) with n= 0, 1, 2, ... The momentum operator, p can be expressed as -i Pr = A √za ( - ¹), 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 (pr) = 0 in the state ₁(x). (b) Given that ħ² P (ÂÂ' + ¹——Â'¹), = - 2a² where a is a constant, calculate (p2) in the state ₁(x).