chapter  5
- Exactly Solvable Systems II: Scattering States
Pages 32

In the previous chapter we focused our discussion on certain exactly solvable quantum mechanical systems possessing bound states. In the present chapter we wish to concentrate on some fascinating and interesting one-dimensional systems where the quantum states are essentially scattering states. For scattering states energy eigenvalues are continuous and energy eigenfunctions are nonnormalizable. An interesting feature of many scattering potentials is the occurrence of tunneling. It is the most striking qualitative difference between classical mechanics and quantum mechanics. In tunneling a quantum mechanical particle passes through a region where the potential energy exceeds the total energy of the particle. This phenomenon is impossible in classical mechanics. Classically, a particle is completely reflected from a barrier. Quantum tunneling has many technological applications.