Exact Results in Quantum Theory

I will describe several families of one-dimensional Schrödinger operators, whose eigenfunctions can be expressed in terms of Bessel, or more generally, confluent functions. I will show how to compute their Green functions (the kernel of their resolvents). I will also formulate some open questions (on the geometric interpretation of those operators). My talk will be especially useful to those who teach exercise classes in Quantum Mechanics.