  The finite and infinite square wells are potentials typically discussed in
undergraduate quantum mechanics courses. In this paper, we discuss these
potentials in the light of the recent studies of the modification of the
Heisenberg uncertainty principle into a generalized uncertainty principle as a
consequence of attempts to formulate a quantum theory of gravity. The
fundamental concepts of the minimal length scale and the generalized
uncertainty principle are discussed and the modified energy eigenvalues and
transmission coefficient are derived.
