It seems to me that the intuitive explanation of path integrals in quantum mechanics describes scattering processes only.
You have a particle going from A to B and you compute the probability amplitude to go from A to B.
But in a bound state, such as an infinite potential well or an hydrogen atom, it doesn't seem natural to consider a particle going from one place to other. Specially if the state is stationary.
How is the path integral useful in bound states?