In the spherical square well potential problem, Total energy can be negative out side the well where potential is defined to be zero, how can total energy can be negative out side the well where the is no potential , I'm confused because outside there only kinetic energy
The negative total energy means that the particle is bound to the well. In the finite potential case, there is some probability that the bound particle can be observed outside the potential well even though there is no "Force" present outside.
However, as the particle is bound to the well, as $r$ becomes larger, the probability density of observing bound particle will be smaller. You should not consider the particle as a point mass ,it is a wavefunction spreaded over the entire space.
Positive energy means that the particle is not bound to the potential, and will be able to move freely outside the well.
