ABSTRACT
This chapter discusses energy levels for more realistic systems. It looks at a different class of problems involving the scattering of free particles from a potential. The chapter uses the free-particle wave functions to describe an important physical process – the scattering of a steady beam of particles from a barrier. To get the first one note that cannot step down for ever, for eventually the ground state will be reached. To construct the excited wave functions one must substitute a full polynomial for F in equation and equate the coefficients of all the powers to zero. The rapidly declining tail on a wave function which penetrates into a classically forbidden region of a barrier could, if the barrier were of finite thickness, emerge from the remote side and become wave-like again, representing the tunnelling of particles through the barrier.
