Second-Harmonic Generation Investigated by Topless Potential Well With Inverse Square Root

A short-range topless potential energy with inverse square root is introduced to solve the energy spectrum equations and the bound state wave functions of the static Schr $\ddot {\textrm {o}}$ dinger equation by coordinate variation and combining the extraordinary coefficients of the confluent hypergeometric functions. Furthermore, the model of second-harmonic generation (SHG) with this special potential energy $V(z)$ will appear regular changes. In this letter, we explore the specific characteristics of the second-harmonic generation under the inverse square root potential through multiple factors such as energy intervals and matrix elements.