The problem of local internal waves is studied within an infinite medium with a mean density profile described by a periodic Brunt–Va¨isa¨la¨ frequencyN(z). This appears to be the analog of the quantum‐mechanical problem for a particle in a unidimensional lattice potential. Explicit calculations and detailed analysis are carried out for a delta shapedN2(z) profile, paralleling the so‐called Dirac‐comb model for the quantum crystal. The analysis of this rather special case was motivated by recent oceanographical observations in the Mediterranean showing a sort of periodic behavior in the fine structure of density profiles. The selection of Brillouin zones for the wavenumbers of internal waves and the existence of frequency gaps appear to be the most interesting issues of the study of the dispersion relation. Corrections for a finite depth of the ocean and for a finite extent of the density gradients are also suggested.