I'm an A-level student (I don't know what the US equivalent is sorry, I'm not an undergraduate is what I'm saying), and I've independently done a project on wave functions for a few simple stationary systems; particle in a box and quantum harmonic oscillator are the ones I focused on in the end. However something's been troubling me lately. I've solved the time-independent Schrodinger equation, and I have a series of energy eigenvalues and corresponding eigenfunctions. But what do these actually mean? I know the wave function can be interpreted as a probability amplitude and it can be used to find 'expectation values' for position and momentum. One problem I'm considering is modelling a conjugated pi system in a molecule like butadiene using the particle in an (infinite walled) box. Honestly, I'm really very lost. So lost in fact I don't even really know what I'm asking. Even just pointing me towards something specific to research would be a great help for me. Thank you all in advance.