While learning Classical Mechanics, I am confused on nature and application of centrifugal force. In my textbook, it is written that centrifugal force is a pseudo force that, depends on reference frame, but I can't understand that if it is pseudo force then why we feel something pushing us outwar...

I'll talk of single particle Lagrangian in $n$ dimensions. Suppose in a given coordinate system with the coordinates $(q_i)_{i=1}^n$, the Lagrangian is given by $L(\mathbb{q, \dot q}, t)$. Suppose I switch to another reference frame, which has coordinates $(q'_i)_{i=1}^n$. Now the Lagrangian for...

In my atomic physics notes they say In general, filled sub-shells are spherically symmetric and set up, to a good approximation, a central field. However sources such as here say that, even for the case of a single electron in Hydrogen excited to the 2p sub-shell, the electron is really in a sp...