Sean Carroll

Okay, that's important.

So you have some vector in a Hilbert space.

Everyone thinks that you have a vector in a Hilbert space.

That's part of everyone's theory.

The other thing that is part of everyone's version of quantum mechanics is some version of dynamics.

So the vector not only exists, the quantum state not only is there, but it changes over time.

That's what dynamics means.

And that's usually phrased in terms of the Schrodinger equation, but there's other ways to do it.

There's Heisenberg's equations, the von Neumann equation, the path integral, whatever.

Different ways of saying how the quantum state evolves over time.

And one way, by the way, of specifying that information is in terms of the Hamiltonian

of the theory.

The Hamiltonian is a quantum idea that was descended from an analogous classical idea.

And it's basically just asking how much energy is there in different parts of the wave function.

And it turns out the whole point of Schrodinger's equation is that knowing the Hamiltonian

knowing how different quantum states are associated with different possible values of energy is enough to fix the dynamics.

Okay, so sometimes, I'm only telling you this little bit of jargon because sometimes in this game people will use the word Hamiltonian a lot.

That's what they mean.

Hamiltonian is the thing that defines the dynamics of the theory via the Schrodinger equation.

So you have Hilbert space, you have a state, you have dynamics, but then also people say you have observables, right?