Do Problems 16-17, p. 112-113 of Gasiorowicz.
Math Hint: Your algebra will be simpler if you follow the
transfer matrix approach (choosing 
, 
, 
, 
solutions centered on the appropriate boundaries), proceeding outward to
the right from the central region. You now know from
symmetry the proper form to choose in the central region.
Physics Note: You have just made a physical model of the quantum mechanics of the chemical bond. Separately, each of the two wells represents the potential seen by the valence electrons of an atom. Taken together, the two wells represent the potential seen by the valence electrons of a diatomic molecule in which the two atoms are at distance 2b from each other.
