- "Template:Dirac notation" redirects here.
This is for producing templates ((bra)), ((ket)), and ((bra-ket)). It can also produce quantum state vectors in bra–ket notation, using wikicode, ideally with ((math)), as an alternative to LaTeX in <math> mode, but using this template ( ((braket)) ) is more clumsy than the simpler and more directly applicable ((bra)), ((ket)), and ((bra-ket)).
Application[edit]
There are three parameters, use as many as needed in this order:
- Brackets: choose one of:
- bra (for a bra vector),
- ket (for a ket vector),
- bra-ket (for the inner product), or
- Symbol 1:
- if 1 is set to bra or ket: enter the first symbol for the bra or ket,
- if 1 is set to bra-ket: enter the symbol for the bra part of the inner product
- Symbol 2:
- if 1 is set to bra or ket: this parameter is not needed.
- if 1 is set to bra-ket: enter the symbol for the ket part of the inner product
If 1 is set to bra-ket, the symbols are entered in the order they are read, left to right. The symbols can of course be bold, italic, underlined, any unicode symbol, etc.
Examples[edit]
- Ket
A ket can be written: |ψ⟩, that is ((braket|ket|ψ)).
Using ((math)), a ket can be written: |ψ⟩, that is ((math|((braket|ket|ψ)))).
- Bra
A bra can be written: ⟨ψ| = |ψ⟩†, that is ((braket|bra|ψ)) = ((braket|ket|ψ))<sup>†</sup>.
Using ((math)), a bra can be written: ⟨ψ| = |ψ⟩†, that is ((math|((braket|bra|ψ)) ((=)) ((braket|ket|ψ))<sup>†</sup>)).
- Bra-ket
The inner product of the kets |ξ⟩ and |ψ⟩ can be written: ⟨ψ|ξ⟩ = ⟨ξ|ψ⟩†, that is ((braket|bra-ket|ψ|ξ)) = ((braket|bra-ket|ξ|ψ))<sup>†</sup>.
Using ((math)), the inner product of the kets |ξ⟩ and |ψ⟩ can be written: ⟨ψ|ξ⟩ = ⟨ξ|ψ⟩†, that is ((math|((braket|bra-ket|ψ|ξ)) ((=)) ((braket|bra-ket|ξ|ψ))<sup>†</sup>)).
- Outer products
The outer product of the kets |ξ⟩ and |ψ⟩ can be written: |ψ⟩⟨ξ| = [|ξ⟩⟨ψ|]†, that is ((braket|ket|ψ))((braket|bra|ξ)) = [((braket|ket|ξ))((braket|bra|ψ))]<sup>†</sup>.
Using ((math)), the outer product of the kets |ξ⟩ and |ψ⟩ can be written: |ψ⟩⟨ξ| = [|ξ⟩⟨ψ|]†, that is ((braket|ket|ψ))((braket|bra|ξ)) ((=)) [((braket|ket|ξ))((braket|bra|ψ))]<sup>†</sup>.
- Inner products including operators
The inner product of the kets |ξ⟩ and Ĥ|ψ⟩ is written using a bra and ket separately between the operator (there is no third parameter for the operator symbol):
- ⟨ψ|Ĥ|ξ⟩ = ⟨ξ|Ĥ†|ψ⟩,
that is
((braket|bra|ψ))''Ĥ''((braket|ket|ξ)) = ((braket|bra|ξ))''Ĥ''<sup>†</sup>((braket|ket|ψ)).
Using ((math)), the inner product of the kets |ξ⟩ and Ĥ|ψ⟩ is written using a bra and ket separately between the operator:
- ⟨ψ|Ĥ|ξ⟩ = ⟨ξ|Ĥ†|ψ⟩,
that is
((math|((braket|bra|ψ))''Ĥ''((braket|ket|ξ)) ((=)) ((braket|bra|ξ))''Ĥ''<sup>†</sup>((braket|ket|ψ)))).
In wiki-markup rather than LaTeX:
- iħd/dt|Ψ(t)⟩ = Ĥ|Ψ(t)⟩ ↔ −iħ⟨Ψ(t)|d/dt = ⟨Ψ(t)|Ĥ†
that is,
((math|''iħ''((sfrac|''d''|''dt''))((braket|ket|Ψ(''t''))) ((=)) ''Ĥ''((braket|ket|Ψ(''t''))) ↔ −''iħ''((braket|bra|Ψ(''t'')))((sfrac|''d''|''dt'')) ((=)) ((braket|bra|Ψ(''t'')))''Ĥ''<sup>†</sup>))
The tensor product of the kets |ξ⟩ and |ψ⟩ is written using the ket mode only (there is no parameter for tensor products):
- |ξ⟩|ψ⟩ ≡ |ξ⟩ ⊗ |ψ⟩ ≡ |ξ, ψ⟩,
that is
((braket|ket|ξ))((braket|ket|ψ)) ≡ ((braket|ket|ξ)) ⊗ ((braket|ket|ψ)) ≡ ((braket|ket|ξ, ψ)).
Using ((math)), the tensor product of the kets |ξ⟩ and |ψ⟩ is written using the ket mode only:
- |ξ⟩|ψ⟩ ≡ |ξ⟩ ⊗ |ψ⟩ ≡ |ξ, ψ⟩,
that is
((math|((braket|ket|ξ))((braket|ket|ψ)) ≡ ((braket|ket|ξ)) ⊗ ((braket|ket|ψ)) ≡ ((braket|ket|ξ, ψ)))).
See also[edit]
- ((Angle bracket)): surrounding angle brackets
- ((Langle)), ((Rangle)): single angle brackets
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