Operators used without being explained

[Technon]

I started watching the video lecture series here: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/video-lectures/part-1/ I notice that they use the term "operator" without first explaining it. Operators are also not explained (in fact they are not even mentioned) in my course litterature (Physics for Scientists and Engineers, 6th Edition by Paul A. Tipler (Author), Gene Mosca).

Since operators are not explained, it seems one is supposed to understand the subject without knowledge about them? Is it possible?

 

[fresh_42]

I started watching the video lecture series here: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/video-lectures/part-1/ I notice that they use the term "operator" without first explaining it. Operators are also not explained (in fact they are not even mentioned) in my course litterature (Physics for Scientists and Engineers, 6th Edition by Paul A. Tipler (Author), Gene Mosca).

Since operators are not explained, it seems one is supposed to understand the subject without knowledge about them? Is it possible?

Lecture Notes: first document, first page (after introduction)!

 

[Technon]

So operators are just functions

 

[fresh_42]

So operators are just functions

Yes, and usually linear functions. That is they apply to vector spaces. One (normally) says operator instead of transformation, if this vector space itself consists of functions, e.g. smooth functions, or continuous functions, or as in QM square integrable functions. E.g. if we consider $V=C^\infty (\mathbb{R})$ the vector space of all smooth functions in one real variable, then $D=\dfrac{d}{dx}\, : \,f \longmapsto f\,'$ is such a (linear) operator, the differential operator.

Have a read: https://www.physicsforums.com/insights/tell-operations-operators-functionals-representations-apart/

 

[PeterDonis]

So operators are just functions

Yes, and usually linear functions.

With an appropriate interpretation of the term "functions", yes. An operator on a vector space is a mapping of the vector space into itself, i.e., it maps every vector in the vector space into another vector in the vector space (which might, in some cases, be the same vector).

I say this because operators in QM, which are always linear, are often represented by matrices, and most people don't intuitively thing of matrices and functions as being the same thing.