  In this paper, we study a one-dimensional tight-binding model with tunable
incommensurate potentials. Through the analysis of the inverse participation
rate, we uncover that the wave functions corresponding to the energies of the
system exhibit different properties. There exists a critical energy under which
the wave functions corresponding to all energies are extended. On the contrary,
the wave functions corresponding to all energies above the critical energy are
localized. However, we are surprised to find that the critical energy is a
constant independent of the potentials. We use the self-dual relation to solve
the critical energy, namely the mobility edge, and then we verify the
analytical results again by analyzing the spatial distributions of the wave
functions. Finally, we give a brief discussion on the possible experimental
observation of the invariable mobility edge in the system of ultracold atoms in
optical lattices.
