Difference between revisions of "Template:Braket/doc"
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| − | + | {{Documentation subpage}} | |
| + | <!-- Categories and interwikis go at the bottom of this page. --> | ||
| + | :''"Template:Dirac notation" redirects here.'' | ||
| + | |||
| + | This is for producing templates {{tl|bra}}, {{tl|ket}}, and {{tl|bra-ket}}. It can also produce [[quantum state]] vectors in [[bra–ket notation]], using wikicode, ideally with {{tl|math}}, as an alternative to [[LaTeX]] in <nowiki><math></nowiki> mode, but using this template ( <nowiki>{{braket}}</nowiki> ) is more clumsy than the simpler and more directly applicable <nowiki>{{bra}}, {{ket}}, and {{bra-ket}}</nowiki>. | ||
| + | |||
| + | ==Application== | ||
| + | There are three parameters, use as many as needed in this order: | ||
| + | <!---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> | ||
| + | <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>''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 | ||
| + | </li> | ||
| + | <li>''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 | ||
| + | </li> | ||
| + | </ol> | ||
| + | |||
| + | 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'', <u>underlined<u>, any [[unicode]] symbol, etc. | ||
| + | |||
| + | ==Examples== | ||
| + | ;Ket | ||
| + | |||
| + | A ket can be written: {{braket|ket|ψ}}, that is <code><nowiki>{{braket|ket|ψ}}</nowiki></code>. | ||
| + | |||
| + | Using {{tl|math}}, a ket can be written: {{math|{{braket|ket|ψ}}}}, that is <code><nowiki>{{math|{{braket|ket|ψ}}}}</nowiki></code>. | ||
| + | |||
| + | ;Bra | ||
| + | |||
| + | A bra can be written: {{braket|bra|ψ}} = {{braket|ket|ψ}}<sup>†</sup>, that is <code><nowiki>{{braket|bra|ψ}} = {{braket|ket|ψ}}<sup>†</sup></nowiki></code>. | ||
| + | |||
| + | Using {{tl|math}}, a bra can be written: {{math|{{braket|bra|ψ}} {{=}} {{braket|ket|ψ}}<sup>†</sup>}}, that is <code><nowiki>{{math|{{braket|bra|ψ}} {{=}} {{braket|ket|ψ}}<sup>†</sup>}}</nowiki></code>. | ||
| + | |||
| + | ;Bra-ket | ||
| + | |||
| + | The [[Bra–ket notation#Inner products and bras|inner product]] of the kets {{braket|ket|ξ}} and {{braket|ket|ψ}} can be written: {{braket|bra-ket|ψ|ξ}} = {{braket|bra-ket|ξ|ψ}}<sup>†</sup>, that is <code><nowiki>{{braket|bra-ket|ψ|ξ}} = {{braket|bra-ket|ξ|ψ}}<sup>†</sup></nowiki></code>. | ||
| + | |||
| + | Using {{tl|math}}, the inner product of the kets {{math|{{braket|ket|ξ}}}} and {{math|{{braket|ket|ψ}}}} can be written: {{math|{{braket|bra-ket|ψ|ξ}} {{=}} {{braket|bra-ket|ξ|ψ}}<sup>†</sup>}}, that is <code><nowiki>{{math|{{braket|bra-ket|ψ|ξ}} {{=}} {{braket|bra-ket|ξ|ψ}}<sup>†</sup>}}</nowiki></code>. | ||
| + | |||
| + | ;Outer products | ||
| + | |||
| + | The [[Bra–ket notation#Outer products|outer product]] of the kets {{braket|ket|ξ}} and {{braket|ket|ψ}} can be written: {{braket|ket|ψ}}{{braket|bra|ξ}} = [{{braket|ket|ξ}}{{braket|bra|ψ}}]<sup>†</sup>, that is <code><nowiki>{{braket|ket|ψ}}{{braket|bra|ξ}} = [{{braket|ket|ξ}}{{braket|bra|ψ}}]<sup>†</sup></nowiki></code>. | ||
| + | |||
| + | Using {{tl|math}}, the outer product of the kets {{math|{{braket|ket|ξ}}}} and {{math|{{braket|ket|ψ}}}} can be written: {{math|{{braket|ket|ψ}}{{braket|bra|ξ}} {{=}} [{{braket|ket|ξ}}{{braket|bra|ψ}}]<sup>†</sup>}}, that is <code><nowiki>{{braket|ket|ψ}}{{braket|bra|ξ}} {{=}} [{{braket|ket|ξ}}{{braket|bra|ψ}}]<sup>†</sup></nowiki></code>. | ||
| + | |||
| + | ;Inner products including [[operator (physics)|operator]]s | ||
| + | |||
| + | The inner product of the kets {{braket|ket|ξ}} and ''Ĥ''{{braket|ket|ψ}} is written using a bra and ket separately between the operator (there is no third parameter for the operator symbol): | ||
| + | :{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} = {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}, | ||
| + | that is | ||
| + | :<code><nowiki>{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} = {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}</nowiki></code>. | ||
| + | |||
| + | Using {{tl|math}}, the inner product of the kets {{math|{{braket|ket|ξ}}}} and {{math|''Ĥ''{{braket|ket|ψ}}}} is written using a bra and ket separately between the operator: | ||
| + | :{{math|{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} {{=}} {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}}}, | ||
| + | that is | ||
| + | :<code><nowiki>{{math|{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} {{=}} {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}}}</nowiki></code>. | ||
| + | |||
| + | ;[[Schrödinger equation]]: | ||
| + | In wiki-markup rather than LaTeX: | ||
| + | :{{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>}} | ||
| + | that is, | ||
| + | :<code><nowiki>{{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>}}</nowiki></code> | ||
| + | |||
| + | ;[[Bra–ket notation#Composite bras and kets|Tensor products]]: | ||
| + | |||
| + | The [[tensor product]] of the kets {{braket|ket|ξ}} and {{braket|ket|ψ}} is written using the ket mode only (there is no paramter for tensor products): | ||
| + | :{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}⊗{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}, | ||
| + | that is | ||
| + | :<code><nowiki>{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}&otimes;{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}</nowiki></code>. | ||
| + | |||
| + | Using {{tl|math}}, the tensor product of the kets {{math|{{braket|ket|ξ}}}} and {{math|{{braket|ket|ψ}}}} is written using the ket mode only: | ||
| + | :{{math|{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}⊗{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}}}, | ||
| + | that is | ||
| + | :<code><nowiki>{{math|{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}&otimes;{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}}}</nowiki></code>. | ||
| + | |||
| + | ==See also== | ||
| + | |||
| + | * {{tl|Angle bracket}}: surrounding angle brackets | ||
| + | * {{tl|Langle}}, {{tl|Rangle}}: single angle brackets | ||
| + | |||
| + | {{Math templates|notation}} | ||
| + | |||
| + | <includeonly> | ||
| + | {{#ifeq:{{PAGENAME}}|Braket| | ||
| + | <!-- Categories go here --> | ||
| + | [[Category:Mathematical formatting templates]] | ||
| + | [[Category:Physics templates]] | ||
| + | }}</includeonly> | ||
Revision as of 22:05, 13 August 2016
| 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
- {{Angle bracket}}: surrounding angle brackets
- {{Langle}}, {{Rangle}}: single angle brackets