Difference between revisions of "Template:Braket/doc"
imported>SporkBot m (Update template name) |
|||
| Line 9: | Line 9: | ||
<!---THESE ARE NOT SPELLING MISTAKES - THEY ARE ACTUALLY USED IN THE TEMPLATE PARAMETERS - PLEASE DON'T "CORRECT" THE SPELLING (SAY) "BRAKET" TO "BRACKET" - THANKS!!!---> | <!---THESE ARE NOT SPELLING MISTAKES - THEY ARE ACTUALLY USED IN THE TEMPLATE PARAMETERS - PLEASE DON'T "CORRECT" THE SPELLING (SAY) "BRAKET" TO "BRACKET" - THANKS!!!---> | ||
<ol> | <ol> | ||
| − | <li> | + | <li>''Brackets:'' choose one of: |
| − | * | + | *''bra'' (for a bra vector), |
| − | * | + | *''ket'' (for a ket vector), |
| − | * | + | *''bra-ket'' (for the [[Bra–ket notation#Inner products and bras|inner product]]), or |
| − | <li> | + | </li> |
| + | <li>''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'' 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</li> | + | *if 1 is set to ''bra-ket'': enter the symbol for the ''bra'' part of the inner product |
| − | <li> | + | </li> |
| + | <li>''Symbol 2:'' | ||
*if 1 is set to ''bra'' or ''ket'': this parameter is not needed. | *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</li> | + | *if 1 is set to ''bra-ket'': enter the symbol for the ''ket'' part of the inner product |
| + | </li> | ||
</ol> | </ol> | ||
Revision as of 04:09, 10 July 2015
| This is a documentation subpage for Template:Braket. It contains usage information, categories and other content that is not part of the original template page. |
- "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
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
- 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>}}.
- Bra-ket
The inner product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: ⟨ψ|ξTemplate:Rangle = ⟨ξ|ψTemplate:Rangle†, that is {{braket|bra-ket|ψ|ξ}} = {{braket|bra-ket|ξ|ψ}}<sup>†</sup>.
Using {{math}}, the inner product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: ⟨ψ|ξTemplate:Rangle = ⟨ξ|ψTemplate:Rangle†, that is {{math|{{braket|bra-ket|ψ|ξ}} {{=}} {{braket|bra-ket|ξ|ψ}}<sup>†</sup>}}.
- Outer products
The outer product of the kets |ξTemplate:Rangle and |ψTemplate:Rangle can be written: |ψTemplate:Rangle⟨ξ| = [|ξTemplate:Rangle⟨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 |ξTemplate:Rangle and |ψTemplate:Rangle can be written: |ψTemplate:Rangle⟨ξ| = [|ξTemplate:Rangle⟨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 |ξTemplate:Rangle and Ĥ|ψTemplate:Rangle is written using a bra and ket separately 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 separately 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