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Diffstat (limited to 'latex/know/concept/dirac-notation/source.md')
| -rw-r--r-- | latex/know/concept/dirac-notation/source.md | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/latex/know/concept/dirac-notation/source.md b/latex/know/concept/dirac-notation/source.md index 47aa370..f34047d 100644 --- a/latex/know/concept/dirac-notation/source.md +++ b/latex/know/concept/dirac-notation/source.md @@ -3,18 +3,18 @@ # Dirac notation -*Dirac notation* is a notation to do calculations in a Hilbert space +**Dirac notation** is a notation to do calculations in a Hilbert space without needing to worry about the space's representation. It is basically the *lingua franca* of quantum mechanics. -In Dirac notation there are *kets* $\ket{V}$ from the Hilbert space -$\mathbb{H}$ and *bras* $\bra{V}$ from a dual $\mathbb{H}'$ of the +In Dirac notation there are **kets** $\ket{V}$ from the Hilbert space +$\mathbb{H}$ and **bras** $\bra{V}$ from a dual $\mathbb{H}'$ of the former. Crucially, the bras and kets are from different Hilbert spaces and therefore cannot be added, but every bra has a corresponding ket and vice versa. -Bras and kets can only be combined in two ways: the *inner product* -$\braket{V}{W}$, which returns a scalar, and the *outer product* +Bras and kets can be combined in two ways: the **inner product** +$\braket{V}{W}$, which returns a scalar, and the **outer product** $\ket{V} \bra{W}$, which returns a mapping $\hat{L}$ from kets $\ket{V}$ to other kets $\ket{V'}$, i.e. a linear operator. Recall that the Hilbert inner product must satisfy: |