9. Continuous Variables (IV)

In this lecture, I’ve shown that it is possible to upgrade some symmetric operators to self-adjoint ones by expanding their domain of defitnition through an example (momentum operator in finite region). Then investigated their physical significance and how their show-up in Aharonov-Bohm effect. Then, I’ve shown that this is not always possible (with a simple counter example: radial momentum) and some symmetric operators cannot become self-adjoint in any ways! Now, we’ve delved into uncertainty relations. I’ve reviewed the formal derivation of them to be aware of mathematical assumptions behind each step for futher investigations.