Learning derivations versus solving problems

[spaghetti3451]

Hi, I understand when I study a physics topic, it's very important that I solve as many problems as I can possibly can and it's also very important to internalise all the techniques used to solve problems in that topic.

However, I was wondering if the same applies for the derivation of formulae that precedes the exercises in textbooks. I know that it's good to understand the derivation of the different formulae, but would you say that I would also have to internalise the steps used to derive the formulae.

For example, I'd be able to solve time-independent pertubation problems without any mistakes if you wake me up at four o'clock in the morning, but in deriving the corrections to the pertubed eigenvalues and eigenfunctions, I'd get stuck and make tonnes of mistakes along the way.

 

[jedishrfu]

Deriving the formula is a kind of boundary value problem ie the formulas come out of certain restrictions posed. It's really useful to understand this as it comes up in real world problems where you must decide what principles to use and what constraints are present.