# Generator of rotations rotations of WHAT?

1. Jul 20, 2009

### AxiomOfChoice

"Generator of rotations"...rotations of WHAT?

The angular momentum operator is defined as the "generator of rotations." Fine. But rotations of WHAT? What's being rotated? The wave function (doesn't make sense; isn't the wave function a scalar), perhaps? An arbitrary vector in the coordinate system under investigation?

2. Jul 20, 2009

### CompuChip

Re: "Generator of rotations"...rotations of WHAT?

It is the latter. Equivalently, you are rotating the basis of the three-dimensional space (a passive rotation). Or, yet differently formulated, you are rotating the space itself while keeping the basis fixed (active rotation), which also causes the coordinates of vectors to change.

3. Jul 20, 2009

### DrFaustus

Re: "Generator of rotations"...rotations of WHAT?

AxiomOfChoice -> Rotations of yourself... or of your coordinate system, if you prefer. To which correspond transformations of observables/states. And the wave function is nothing but an explicit representation of a vector in some specific base (the "coordinate representation").

4. Jul 20, 2009

### AxiomOfChoice

Re: "Generator of rotations"...rotations of WHAT?

Right now, I'm studying a triatomic molecule confined to move in two dimensions. Suppose the central nucleus is fixed at the origin, and let $\theta$ be the angle between the radius vector of the first (free to move) nucleus and the second (free to move) nucleus. How do I show that $L = -i\hbar \dfrac{\partial}{\partial \theta}$ in this case?

5. Jul 21, 2009

### xepma

Re: "Generator of rotations"...rotations of WHAT?

Use the definition of L:
L = r x p (outer product)