Hooke's law: Constructing a force operator for electron orbitals?

[Vectronix]

TL;DR

Wondering if the information in my post is like Hooke's Law for electron orbitals or part of it

I saw a post on Facebook about Hooke's Law. F = -kx + mg. Does that mean a "force operator" could be constructed... if the wave function has eigenfunctions equal to some constant times e^{kr + iωt} could the observed components of F (a force between an electron and a proton, let's say) be defined as the natural logarithm of Ψ? I think I'm using the right terminology but please correct me if I'm wrong.

 

[anuttarasammyak]

You use alphabet k to mean two different quantities i.e., spring constant and wave number, which cause the confusion.