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Semiconductor heterostructures with prescribed energy dependence of thetransmittance can be designed by combining: {\em a)} Pad\'e approximantreconstruction of the S-matrix; {\em b)} inverse scattering theory forSchro\"dinger's equation; {\em c)} a unitary transformation which takes intoaccount the variable mass effects. The resultant continuous concentrationprofile can be digitized into an easily realizable rectangular-wells structure.For illustration, we give the specifications of a 2 narrow band-pass 12 layer$Al_cGa_{1-c}As$ filter with the high energy peak more than {\em twicenarrower} than the other.Comment: 4 pages, Revtex with one eps figur

Electron wave filters from inverse scattering theory