SOLUTION OF THE ONE-DIMENSIONAL SCHRODINGER-EQUATION IN AN ARBITRARY PERIODIC POTENTIAL

A new approach is presented for one-dimensional band structure calculation in which a periodic potential is approximated by a sequence of constant height segments. The overall condition for allowed energy bands reduces to the fundamental inequality -2 less-than-or-equal-to Tr-PI less-than-or-equal-to 2 where PI is the product of a chain of 2 x 2 matrices with one matrix pertinent to each segment of a period. This leads to a straightforward computational procedure that does not require an exposure to the conventional methods of solid state theory. For an arbitrarily shaped potential the precision of our resulting band structure depends on only the number of segments chosen.