Basis Sets


In words, how would you compare the idea of a basis set from quantum to vector space?


A basis set of a quantum mechanical observable is a complete set of orthonormal eigenfunctions built up from the eigenfunctions of that observable. If two observables share a common basis set they commute.

A basis set of a finite dimensional vector space is the a set of linearly independent vectors that span the space.

It is not obvious that the two uses of the words "basis set" are related but fundamentally they convey the same idea. Any element of a vector space may be expressed in terms of the basis set. Any element of a commuting set of observables may have its eigenfunctions expressed as a well defined function of eigenfunctions of the basis set.

As I re-read this it strikes me that this is a real stretch, but it is the best I can do short of too much research. I am curious how you got to this question from the courses you signed up for. Is this possibly an exam for the instructor?:).

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.