Difference between revisions of "Template:Braket/doc"

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imported>Quondum
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imported>Maschen
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*'''bra''' (for a bra vector),  
 
*'''bra''' (for a bra vector),  
 
*'''ket''' (for a ket vector),
 
*'''ket''' (for a ket vector),
*'''braket''' (for the [[Bra–ket notation#Inner products and bras|inner product]]), or
+
*'''bra-ket''' (for the [[Bra–ket notation#Inner products and bras|inner product]]), or
*'''ketbra''' (for the [[Bra–ket notation#Outer products|outer product]]).</li>
 
 
<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 ''braket'' or ''ketbra'': enter the symbol for the ''bra'' part of the inner product, or ''ket'' part of the outer product.</li>
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*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 ''braket'' or ''ketbra'': enter the symbol for the ''ket'' part of the inner product, or ''bra'' part of the outer product.</li>
+
*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 ''braket'' or ''ketbra'', 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.  
+
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==
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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>.
  
;Braket
+
;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|braket|ψ|ξ}} = {{braket|braket|ξ|ψ}}<sup>†</sup>, that is <code><nowiki>{{braket|braket|ψ|ξ}} = {{braket|braket|ξ|ψ}}<sup>†</sup></nowiki></code>.
+
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|braket|ψ|ξ}} {{=}} {{braket|braket|ξ|ψ}}<sup>†</sup>}}, that is <code><nowiki>{{math|{{braket|braket|ψ|ξ}} {{=}} {{braket|braket|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>.
  
;Ketbra
+
;Outer products
  
The [[Bra–ket notation#Outer products|outer product]] of the kets {{braket|ket|ξ}} and {{braket|ket|ψ}} can be written: {{braket|ketbra|ψ|ξ}} = [{{braket|ketbra|ξ|ψ}}]<sup>†</sup>, that is <code><nowiki>{{braket|ketbra|ψ|ξ}} = [{{braket|ketbra|ξ|ψ}}]<sup>†</sup></nowiki></code>.
+
The [[Bra–ket notation#Outer products|outer product]] of the kets {{braket|ket|ξ}} and {{braket|ket|ψ}} can be written: {{braket|ket}}{{braket|bra|ξ}} = [{{braket|ket}}{{braket|bra|ψ}}]<sup>†</sup>, that is <code><nowiki>{{braket|ket}}{{braket|bra|ξ}} = [{{braket|ket}}{{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|ketbra|ψ|ξ}} {{=}} [{{braket|ketbra|ξ|ψ}}]<sup>†</sup>}}, that is <code><nowiki>{{math|{{braket|ketbra|ψ|ξ}} {{=}} [{{braket|ketbra|ξ|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}}{{braket|bra|ξ}} {{=}} [{{braket|ket}}{{braket|bra|ψ}}]<sup>†</sup>}}, that is <code><nowiki>{{braket|ket|ψ}}{{braket|bra|ξ}} {{=}} [{{braket|ket}}{{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

"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:

  1. Brackets: choose one of:
    • bra (for a bra vector),
    • ket (for a ket vector),
    • bra-ket (for the inner product), or
  2. 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
  3. 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: Template:Rangle, that is {{braket|ket|ψ}}.

Using {{math}}, a ket can be written: Template:Rangle, that is {{math|{{braket|ket|ψ}}}}.

Bra

A bra can be written: ⟨ψ| = Template:Rangle, that is {{braket|bra|ψ}} = {{braket|ket|ψ}}<sup>†</sup>.

Using {{math}}, a bra can be written: ⟨ψ| = Template:Rangle, that is {{math|{{braket|bra|ψ}} {{=}} {{braket|ket|ψ}}<sup>†</sup>}}.

Bra-ket

The inner product of the kets Template:Rangle and Template: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 Template:Rangle and Template: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 Template:Rangle and Template:Rangle can be written: Template:Rangle⟨ξ| = [Template: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 Template:Rangle and Template:Rangle can be written: Template:Rangle⟨ξ| = [Template: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 Template:Rangle and ĤTemplate:Rangle is written using a bra and ket seperatley between the operator (there is no third parameter for the operator symbol):

⟨ψ|ĤTemplate:Rangle = ⟨ξ|ĤTemplate: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 Template:Rangle and ĤTemplate:Rangle is written using a bra and ket seperatley between the operator:

⟨ψ|ĤTemplate:Rangle = ⟨ξ|ĤTemplate:Rangle,

that is

{{math|{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} {{=}} {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}}}.
Schrödinger equation

In wiki-markup rather than LaTeX:

Template:Sfrac|Ψ(t)Template:Rangle = Ĥ|Ψ(t)Template:Rangle ↔ −⟨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>}}
Tensor products

The tensor product of the kets Template:Rangle and Template:Rangle is written using the ket mode only (there is no paramter for tensor products):

Template:RangleTemplate:RangleTemplate:RangleTemplate:Rangle|ξ, ψTemplate:Rangle,

that is

{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}&otimes;{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}.

Using {{math}}, the tensor product of the kets Template:Rangle and Template:Rangle is written using the ket mode only:

Template:RangleTemplate:RangleTemplate:RangleTemplate:Rangle|ξ, ψTemplate:Rangle,

that is

{{math|{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}&otimes;{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}}}.

See also