- #1
\displaystyle R_{\mu v} - \frac{1}{2} R g_{\mu v} + \Lambda g_{\mu v} = \frac{8 \pi G}{c^4} T_{\mu v}
\displaystyle i \hbar\frac{\partial \psi}
{\partial t}=
\frac{-\hbar^2}{2m}
\left(\frac{\partial^2}{\partial x^2}
+ \frac{\partial^2}{\partial y^2}
+ \frac{\partial^2}{\partial z^2}
\right) \psi + V \psi.
What do you mean by required? If you are doing an exam you might speak of requirements. Otherwise what is "required" is just that you convince yourself that it is true. Note that there is no need to pull the metrics out of the ##F_{\alpha\beta}## in your second term. The indices will be raised by the metrics from the ##F^{\alpha\beta}## once you pull them out of the derivative.Is this working required for a beginner or is it to be left out?
What do you mean by required?