- #1

## Main Question or Discussion Point

Good morning!

I have a problem in understanding the steps from vectors to operators.

Imagine you are given a vectorial observable.

In classical mechanics, after rotating the system it transform with a rotation matrix R.

If we go to quantum mechanics, this observable becomes an operator that is not obvious to transform with the same law.

Imagine for example the momentum: in classical mechanics it is clearly a vector, but when we go to quantum mechanics it becomes a gradient, so it will transform differently when rotating the system of reference.

How is this possible?

I have a problem in understanding the steps from vectors to operators.

Imagine you are given a vectorial observable.

In classical mechanics, after rotating the system it transform with a rotation matrix R.

If we go to quantum mechanics, this observable becomes an operator that is not obvious to transform with the same law.

Imagine for example the momentum: in classical mechanics it is clearly a vector, but when we go to quantum mechanics it becomes a gradient, so it will transform differently when rotating the system of reference.

How is this possible?