Template:Braket
- "Template:Dirac notation" redirects here.
This is for producing templates{{bra}},{{ket}},and{{bra-ket}}.It can also producequantum statevectors inbra–ket notation,using wikicode, ideally with{{math}},as an alternative toLaTeXin <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 theinner product), or
- Symbol 1:
- if 1 is set tobraorket:enter the first symbol for the bra or ket,
- if 1 is set tobra-ket:enter the symbol for thebrapart of the inner product
- Symbol 2:
- if 1 is set tobraorket:this parameter is not needed.
- if 1 is set tobra-ket:enter the symbol for theketpart of the inner product
If 1 is set tobra-ket,the symbols are entered in the order they are read, left to right. The symbols can of course bebold,italic,underlined,anyunicodesymbol, 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
Theinner productof 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
Theouter productof 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 includingoperators
The inner product of the kets|ξ⟩andĤ|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⟩andĤ|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>}}
Thetensor productof 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