  Electronic Structure Theory (EST) describes the behavior of electrons in
matter and is used to predict material properties. Conventionally, this
involves forming a Hamiltonian and solving the Schr\"odinger equation through
discrete computation. Here, a new perspective to EST is provided by treating a
perfectly crystalline material as a Linear Translation Invariant (LTI) system.
The validity of this LTI-EST formalism is demonstrated by determining band
structures for a one-dimensional chain of atoms, including the phenomenon of
band structure folding in super cells. The proposed formalism allows for
analytical traceability of band structure folding and offers computational
advantage by bypassing the O(N) eigenvalue calculations. The spike-based
computing nature of the proposed LTI-EST formalism is highlighted; thereby
implying potential for material simulations solely in the spiking domain.
