Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

Based on the operator Hermite polynomials method (OHPM), we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications. As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.