Template:Braket/doc
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- "Template:Dirac notation" redirects here.
This is for producing quantum state vectors in bra–ket notation, using wikicode, ideally with {{math}}, as an alternative to LaTeX in <math> mode.
Application
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),
- braket (for the inner product), or
- ketbra (for the outer product).
- Symbol 1:
- if 1 is set to bra or ket: enter the first symbol for the bra or ket,
- if 1 is set to braket or ketbra: enter the symbol for the bra part of the inner product, or ket part of the outer product.
- Symbol 2:
- if 1 is set to bra or ket: this parameter is not needed.
- if 1 is set to braket or ketbra: enter the symbol for the ket part of the inner product, or bra part of the outer product.
If 1 is set to braket or ketbra, 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
- Ket
A ket can be written: |ψTemplate:Rangle, that is {{braket|ket|ψ}}.
Using {{math}}, a ket can be written: |ψTemplate:Rangle, that is {{math|{{braket|ket|ψ}}}}.
- Bra
A bra can be written: ⟨ψ| = |ψTemplate:Rangle†, that is {{braket|bra|ψ}} = {{braket|ket|ψ}}<sup>†</sup>.
Using {{math}}, a bra can be written: ⟨ψ| = |ψTemplate:Rangle†, that is {{math|{{braket|bra|ψ}} {{=}} {{braket|ket|ψ}}<sup>†</sup>}}.
- Braket
The inner product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: = †, that is {{braket|braket|ψ|ξ}} = {{braket|braket|ξ|ψ}}<sup>†</sup>.
Using {{math}}, the inner product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: = †, that is {{math|{{braket|braket|ψ|ξ}} {{=}} {{braket|braket|ξ|ψ}}<sup>†</sup>}}.
- Ketbra
The outer product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: = []†, that is {{braket|ketbra|ψ|ξ}} = [{{braket|ketbra|ξ|ψ}}]<sup>†</sup>.
Using {{math}}, the outer product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: = []†, that is {{math|{{braket|ketbra|ψ|ξ}} {{=}} [{{braket|ketbra|ξ|ψ}}]<sup>†</sup>}}.
- Inner products including operators
The inner product of the kets |ξTemplate:Rangle and Ĥ|ψTemplate:Rangle is written using a bra and ket seperatley between the operator (there is no third parameter for the operator symbol):
- ⟨ψ|Ĥ|ξTemplate:Rangle = ⟨ξ|Ĥ†|ψTemplate:Rangle,
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 |ξTemplate:Rangle and Ĥ|ψTemplate:Rangle is written using a bra and ket seperatley between the operator:
- ⟨ψ|Ĥ|ξTemplate:Rangle = ⟨ξ|Ĥ†|ψTemplate:Rangle,
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:
- iħTemplate:Sfrac|Ψ(t)Template:Rangle = Ĥ|Ψ(t)Template:Rangle ↔ −iħ⟨Ψ(t)|Template:Sfrac = ⟨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 |ξTemplate:Rangle and |ψTemplate:Rangle is written using the ket mode only (there is no paramter for tensor products):
- |ξTemplate:Rangle|ψTemplate:Rangle ≡ |ξTemplate:Rangle⊗|ψTemplate:Rangle ≡ |ξ, ψTemplate:Rangle,
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 |ξTemplate:Rangle and |ψTemplate:Rangle is written using the ket mode only:
- |ξTemplate:Rangle|ψTemplate:Rangle ≡ |ξTemplate:Rangle⊗|ψTemplate:Rangle ≡ |ξ, ψTemplate:Rangle,
that is
{{math|{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}⊗{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}}}.
See also
- Template:Braket/sandbox
- {{rangle}}
- {{langle}}