Difference between revisions of "Template:Braket/doc"
imported>Quondum (n-dash) |
imported>Maschen (update) |
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| Line 14: | Line 14: | ||
*'''bra''' (for a bra vector), | *'''bra''' (for a bra vector), | ||
*'''ket''' (for a ket vector), | *'''ket''' (for a ket vector), | ||
| − | *''' | + | *'''bra-ket''' (for the [[Bra–ket notation#Inner products and bras|inner product]]), or |
| − | |||
<li>'''''Symbol 1:''''' | <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 '' | + | *if 1 is set to ''bra-ket'': enter the symbol for the ''bra'' part of the inner product</li> |
<li>'''''Symbol 2:''''' | <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 '' | + | *if 1 is set to ''bra-ket'': enter the symbol for the ''ket'' part of the inner product</li> |
</ol> | </ol> | ||
| − | If 1 is set to '' | + | 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== | ==Examples== | ||
| Line 40: | Line 39: | ||
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>. | 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| | + | 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| | + | 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| | + | 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| | + | 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 | ;Inner products including [[operator (physics)|operator]]s | ||
Revision as of 05:47, 15 April 2013
| 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 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),
- 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 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}}