Part 1 of a series exploring the quantum mechanics of guinea pigs, with a short digression into creation and annihilation operators and their uses in guinea pig quantum mechanics.
The spot where this lost me a tad is when you introduced a_hat_dagger. An explanation of that meant would have been helpful. I was thinking of them as separate (dagger == jump up a state, hat == jump down a state). But it wasn’t explained exactly what it means for the a vector to have both symbols so I was left to guess. Any help with what they mean?
The spot where this lost me a tad is when you introduced a_hat_dagger. An explanation of that meant would have been helpful. I was thinking of them as separate (dagger == jump up a state, hat == jump down a state). But it wasn’t explained exactly what it means for the a vector to have both symbols so I was left to guess. Any help with what they mean?
Oh, sure! I'll add a clarification table.
hat = is a matrix, distinct from a vector or a number.
dagger = complex conjugate + transpose of matrix or vector.
hat{a} = jump down a state. hat{a}^dagger = jump up a state.
It's a nice property of the ladder operators that the creation operator is the complex transpose of the annihilation operator.
Does that help?