Although I do not have much interest in the Schrodinger equation, it is nice to see mathematicians write about Schrodinger equation. Most fundamental physicist are generally happy with non relativistic quantum mechanics. However for many mathematicians Schrodinger’s equation is an interesting PDE and Terrence Tao notes how he is interested in non linear Schrodinger equation. Here is  Tao’s blog link which has a link to his article on Schrodinger’s equation.