To my understanding, when a particle is in a bound state, it is "stuck" because its total energy is less than the surrounding potential. I am confused on how to prove a particular potential has no bound states. For example, in one problem, I am asked to show that there is no bound state in a spherical finite well, if the potential inside the well is less than some quantity. I guess I would like to know what a bound state "looks" like mathematically. In a simple case like the harmonic oscillator, I can see what the bound state is, but I do not know how to show that they are bound states. This is what I need help with for the case of a finite spherical well.