What does the hat signify?

1. Aug 2, 2010

amorrow

This is a beginner's question: what does that hat about the H (Hamiltonian) symbol signify? One often sees it in the Schrödinger equation and a few other symbols such as the p of momentum.

Last edited: Aug 2, 2010
2. Aug 2, 2010

jcsd

Two different things is the answer. The caret above the Hamiltonian tells you that it's an operator, the caret above a momentum vector tells you that this specific vector is a unit vector.

3. Aug 2, 2010

Fredrik

Staff Emeritus
Are you sure about that last one? $\hat p=-i\hbar\frac{d}{dx}$ is certainly an operator. The hat is there because the author wants to be able to write things like

$$\hat p e^{ipx/\hbar}=pe^{ipx/\hbar}$$

Amorrow, a lot of books don't use the "hat" notation. For example, Weinberg writes this $\hat p$ as P instead, and Sakurai writes it as p. Sakurai writes p' for what I called p above.

4. Aug 3, 2010

jcsd

Yes, if the the momentum is the momentum operator, then the caret means it's an operator. Tbh actually thinking about it, it's far more likely that the symbol amorrow saw was meant to represent the momentum operator.

5. Aug 3, 2010

amorrow

Yes, I was looking at the Wikipedia entry on momentum operator, etc. Their use of the caret/hat is somewhat inconsistent.

6. Aug 3, 2010

jcsd

Yep, in a quantum mechanical setting it's going to mean the momentum operator. In a classical kinematic setting it'd probably mean a momentum unit vector.