8. Continuous Variables (III)

In this lecture, I’ve discussed linear operators. I begun by showing that how some innocent-looking finite-dimensional matrices cannot make sense when generalized to infinite dimensions and motivated the ``Domain of Definition” and ``Boundedness” of an operator. Then, defined adjoint operation and the notions of ``Self-Adjoint” & ``Symmetric” operators (and their difference!). Then, I show that momentum operator is not symmetric nor self-adjoint when defined on a finite region! unless it is defined on certain functions satisfying a boundary conditions.