1. The problem statement, all variables and given/known data Part d) of the question below. 2. Relevant equations We are told NOT to use the ladder technique to find the position operator as that's not covered until our Advanced Quantum Mechanics module next year (I don't even know this technique anyway). I emailed my tutor and he said it's about basic understanding of probability density which, according to his lecture notes, is given by P = |φ(x)|2 I'm also using this given information, also from his lectures: 3. The attempt at a solution For parts a, b and c I was fine. For a) I took the derivative of the potential function and used that to find the minimum point, x0, where the particle is in stable equilibrium. For b) I expanded the potential function as a Taylor series and applied the relevant parts to the equation of motion for a harmonic oscillator about the point x0. For part c) I simply found E = E1 - E0 and used that with hc/λ to find the wavelength. But part d).... To be honest I'm totally stuck here and more than a little annoyed at how vague my lecturer has been in his correspondence to me. I don't understand how to use and apply "P = |φ(x)|2" to come to any useful answer. I'm pretty sure I'm supposed to be taking φ(x) = φn(x) = φ1(x) as detailed in the above screenshot, in order to be working with the correct eigenstate for this part of the problem. But from there I really don't know. As far as "P = |φ(x)|2" goes, I'm sure there's a need to normalise it too. In fact I'm sure there's a lot more to it than that, involving some form of P = (x |φ(x)|)2", integrating over infinity, etc... My brain is totally fried right now . Any help would be very much appreciated. Thanks!