Terms of "second order" and "fourth order"...what does this MEAN?! I am reading the paper written by Born and Oppenheimer that explains the development of the Born-Oppenheimer approximation. The paper contains the following cryptic (to me) statement: "The nuclear vibrations correspond to terms of second order and the rotations to fourth order in the energy, while the first and third order terms vanish." What, EXACTLY, is a "term of second order...in the energy?" (Or fourth order, for that matter?) I'm sure this is something I should know from freshman calculus, but this vernacular gets used a lot, and my understanding of it is muddled - it just is. Should I feel bad about this?