Resonant tunneling via a barrier with multiple energy levels point impurity

We propose a theoretical framework for a Multi-Level Point Impurity (MLPI) model that fundamentally resolves the constraints of the traditional single-state Dirac delta potential. Historically, engineering point interactions with multiple bound states required the use of highly singular, pathological derivatives (e.g., δ^″(x)), leading to intractable wavefunction discontinuities. Our model circumvents these complexities by projecting all internal, multi-level interactions onto a single baseline delta function, yielding an analytically pristine, non-Hermitian operator. We derive exact transmission coefficients for this MLPI and apply it to a Resonant Tunneling (RT) scenario within an opaque barrier. By reducing complex spatial boundary-matching to a straightforward algebraic problem, the MLPI demonstrates high quantitative agreement with exact numerical solutions for double-barrier systems. Furthermore, the model introduces a built-in tuning parameter to precisely fit resonance spectral widths, establishing the MLPI as an exceptionally robust, scalable benchmark for complex "sub-grid" structures such as quantum dots and color centers.