In this talk, we review the paper "Sharp local $L^p$ estimates for the Hermite eigenfunctions" by Wang and Zhang. The local $L^p$ bounds of eigenfunctions over geodesic balls on manifolds have been studied by many authors in connection with an investigation of the concentration of the eigenfunctions. We study sharp $L^p$ bounds of the Hermite eigenfunctions over balls. To prove the nontrivial part of the result, we take an approach introduced in the work of Jeong-Lee-Ryu. We study the strategy of the proof by describing the main ideas