Connecting Classical and Quantum Mechanics

When an object moves across the boundary between 2 regions in which it is subject to different (forces / potential energies), the basic behavior of the object is found by solving (N's 2nd Law / the Schroedinger Eqn.).  The (position / wavefunction) of the object is always continuous across the boundary, and the (velocity / derivative dY/dx) is also continuous as long as the (force / change in potential energy) remains finite.

~ Ken Krane, Modern Physics, 1996