Title Shape dependent energy optimization in quantum dots Type of Research Article Keywords Nanostructured quantum dots Minimization problems Eigenvalue problems Abstract In this paper, we investigate a minimization problem related to the principal eigenvalue of the Schrödinger operator. The optimized solution can be applied to design new electronic and photonic devices based on the quantum dots. Researchers (First Researcher)، (Second Researcher)، Hakimeh Mohammadpour (Third Researcher)