  Changes in the metal properties, caused by periodic indents in the metal
surface, have been studied within the limit of quantum theory of free
electrons. It was shown that due to destructive interference of de Broglie
waves, some quantum states inside the low-dimensional metal become quantum
mechanically forbidden for free electrons. Wave vector density in k space,
reduce dramatically. At the same time, number of free electrons does not
change, as metal remains electrically neutral. Because of Pauli exclusion
principle some free electrons have to occupy quantum states with higher wave
numbers. Fermi vector and Fermi energy of low-dimensional metal increase and
consequently its work function decrease. In experiment, magnitude of the effect
is limited by the roughness of metal surface. Rough surface causes scattering
of the de Broglie waves and compromise their interference. Recent experiments
demonstrated reduction of work function in thin metal films, having periodic
indents in the surface. Experimental results are in good qualitative agreement
with the theory. This effect could exist in any quantum system comprising
fermions inside a potential energy box of special geometry.
