Abstract

The forbidden bands of an imperfect, one-dimensional crystal are examined. The existence and number of solutions in each forbidden band is found explicitly for impurity states arising from various types of single impurities, and for Shockley-type surface states arising from models having perfectly terminated surfaces. Also crystals whose only imperfection is an additional attractive or repulsive potential at the surface are examined, and the solutions classified as Tamm-type or Shockley-type surface states.

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