Linear combination 01

I frequently add to our conversations involving the concept of a basis set, or a linear combination of basis functions to describe just about any situation. As a faculty member, my job “wavefunction” includes teaching, scholarship/research, and service. To students, teaching is a clear job function; research in the sciences should also be a clear job function; service is less well defined, but most of you have involvement in running student organizations and this is not too different from a faculty member who serves on, for example, the “curriculum” or “personnel” committee. Mathematically;