Concept of uncertainty is very important.

General mathematics, uncertainly is defined as standard deviation squared, which is intuitively understandable is better than simple standard deviation.

delta function’s fourier form

delta function has eigen vector and value

After math manipulation, it’s an awe to see that the derivative with regard to time is equivalent to momentum, which in classical physics, should be the derivative with regard to time times mass. What an observation!

Noether’s Theorem states:

In QM, operator is corresponding to the measurable, hence the the uncertainty of this metrics:

Sai equation is easier to express in Fourier Series form both for position and for momentum/energy