Undergrad One-Dimensional System: Boundary Condition Applicability

[GANTI_RAVITEJA]

In one dimensional system the boundary condition that the derivative of the wave function Ψ(x) should be continuous at every point is applicable whenever?

 

[hilbert2]

In one dimensional system the boundary condition that the derivative of the wave function Ψ(x) should be continuous at every point is applicable whenever?

It's applicable when the potential energy V(x) is finite everywhere. Counterexamples include the particle in a box and the delta function potential.