  In this paper, by studying a class of 1-D Sturm-Liouville problems with
periodic coefficients, we show and classify the solutions of periodic
Schrodinger equations in a multidimensional case, which tells that not all the
solutions are Bloch solutions. In addition, we also provide several properties
of the solutions and quasimomenta and illustrate the relationship between
bounded solutions and Bloch solutions.
