In this note a one-dimensional band model is proposed based on a periodic Dirac comb having a periodic
mass distribution m(x). The mass function is represented as a Hermitian, non-local separable operator.
Two specific cases–a constant mass model and a sinusoidal mass model–are examined. The lowest
electron and positron bands for the constant mass case are similar to those for the standard relativistic
Kronig-Penney model, suggesting that non-locality has little influence. The results for the sinusoidal case
are consistent with the expectation that at low wavenumber an electron “feels” it has an average constant
mass, but at high wave number, the particle “sees” the periodic mass variation and the band is distorted.
