Just breaking up my questions into sub-questions here. The core of the question is to be found hereI saw an awesome derivation of Schrodinger's equation on Wikipedia. Part of it relies on:
We also know that when $t' = t$, we must have the unitary time evolution operator $U(t, t) = 1$. Therefore, expanding the operator $U(t', t)$ for $t'$ close to $t$, we can write $U(t', t) = 1 - iH(t' - t)$, where $H$ is a Hermitian operator. This follows from the fact that the Lie algebra corresponding to the unitary group comprises Hermitian operators. Taking the limit as the time-difference $t' - t$ becomes very small, we obtain Schrodinger's equation.
What is meant by Lie algebra corresponding to the unitary group comprises Hermitian operators in the derivation in that link?
