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., ), 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.