Difference between revisions of "Template:Langle/doc"

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imported>F=q(E+v^B)
imported>F=q(E+v^B)
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==Examples==
 
==Examples==
  
The template has two main parameters:
+
There is no need to use spaces around the template, due the large spacing in the template glyph.
 
 
* '''out''' - content out of the bracket (i.e. behind the vertex of the bracket)
 
* '''in''' - defualt setting, content in the bracket (i.e. behind the vertex of the bracket),
 
 
 
and an additional parameter '''di''' for an optional delimiter:
 
 
 
* if set to '''bra''' - an additional vertical bar to the right of the content in the bracket appears, to create a bra vector
 
* if left blank it remains as '''in'''.
 
 
 
Usually, there is no need to use the '''out''' parameter, it is optional - typical use may be for a punctuation/coefficient/operation symbol in front of the the vertex. Due to the large spacing in the glyph, it helps to "absorb" the extra space which would displace other characters in front of the vertex away. See the following examples.
 
 
 
;Example of the left angular bracket alone
 
 
 
Notice that {{langle|di=in|in=ψ}} is the same as {{langle|in=ψ}}, becuase '''di''' left blank defualts to '''in'''.
 
 
 
<pre>
 
Notice that {{langle|di=in|in=ψ}} is the same as {{langle|in=ψ}}, becuase '''di''' left blank defualts to '''in'''.
 
</pre>
 
  
 
;Examples of bras
 
;Examples of bras
  
The superposition of states can be written {{langle|di=bra|in=p}} + {{langle|di=bra|in=q}} + {{langle|di=bra|in=χ}} + {{langle|di=bra|in=ψ}}, which is inline with the text.
+
The superposition of states can be written {{langle}}p| +{{langle}}q| +{{langle}}χ| +{{langle}}ψ|, which is inline with the text.
  
Another superposition of states: {{langle|di=bra|in=P}} + {{langle|di=bra|in=Q}} + {{langle|di=bra|in=Φ}} + {{langle|di=bra|in=Ψ}}, again inline.
+
Another superposition of states: {{langle}}P| +{{langle}}Q| +{{langle}}Φ| +{{langle}}Ψ|, again inline.
  
 
<pre>
 
<pre>
The superposition of states can be written {{langle|di=bra|in=p}} + {{langle|di=bra|in=q}} + {{langle|di=bra|in=χ}} +  
+
The superposition of states can be written {{langle}}p| +{{langle}}q| +{{langle}}χ| +{{langle}}ψ|, which is inline with the text.
{{langle|di=bra|in=ψ}}, which is inline with the text.
 
 
 
  
Another superposition of states: {{langle|di=bra|in=P}} + {{langle|di=bra|in=Q}} + {{langle|di=bra|in=Φ}} + {{langle|di=bra|in=Ψ}},  
+
Another superposition of states: {{langle}}P| +{{langle}}Q| +{{langle}}Φ| +{{langle}}Ψ|, again inline.
again inline.
 
 
</pre>
 
</pre>
  
;In conjunction with {{tl|rangle}}:
+
;In conjunction with {{tl|Rangle}}:
  
One sum of inner products is {{langle|di=bra|in=p}}{{rangle|in=q}}+{{langle|di=bra|in=χ}}{{rangle|in=ψ}}, a real number.
+
One sum of inner products is {{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}}, a real number.
  
Another sum of inner products is {{langle|di=bra|in=P}}{{rangle|in=Q}}+{{langle|di=bra|in=Φ}}{{rangle|in=Ψ}}, another real number.
+
Another sum of inner products is {{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}}, another real number.
 
 
A matrix element of operator Ω is {{langle|di=bra|in=ψ}}Ω{{rangle|di=ket|in=ψ}}, and overlapping the states together incorrectly on the same line: {{langle|di=bra|in=ψ{{rangle|in=ψ}}}}, while the correct way is {{langle|in=ψ{{rangle|di=ket|in=ψ}}}}.
 
  
 
<pre>
 
<pre>
One sum of inner products is {{langle|di=bra|in=p}}{{rangle|in=q}}+{{langle|di=bra|in=χ}}{{rangle|in=ψ}}, a real number.
+
{{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}}
 
 
 
 
Another sum of inner products is {{langle|di=bra|in=P}}{{rangle|in=Q}}+{{langle|di=bra|in=Φ}}{{rangle|in=Ψ}}, another real number.
 
 
 
  
A matrix element of operator Ω is {{langle|di=bra|in=ψ}}Ω{{rangle|di=ket|in=ψ}}, and compacting the states together incorrectly on the
+
{{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}}
same line: {{langle|di=bra|in=ψ{{rangle|in=ψ}}}}, while the correct way is {{langle|in=ψ{{rangle|di=ket|in=ψ}}}}.
 
 
</pre>
 
</pre>
  
The average of a quantity ''q'' may be written {{rangle|in={{langle|in=''q''}}}} or identically {{langle|in={{rangle|in=''q''}}}}. The root mean square is then √{{rangle|in={{langle|in=''q''<sup>2</sup>}}}}, i.e. square every value, then average, then take the root.
+
The average of a quantity ''q'' may be written {{langle}}''q''{{rangle}}. The root mean square is then √{{langle}}''q''<sup>2</sup>{{rangle}}, i.e. square every value, then average, then take the root.
  
 
<pre>
 
<pre>
The average of a quantity ''q'' may be written {{rangle|in={{langle|in=''q''}}}} or identically {{langle|in={{rangle|in=''q''}}}}. The  
+
The average of a quantity ''q'' may be written {{langle}}''q''{{rangle}}. The root mean square is  
root mean square is then √{{rangle|in={{langle|in=''q''<sup>2</sup>}}}}, i.e. square every value, then average, then take the root.
+
then √{{langle}}''q''<sup>2</sup>{{rangle}}, i.e. square every value, then average, then take the root.
 
</pre>
 
</pre>
  

Revision as of 08:39, 13 June 2012

This is the left-handed angular bracket used for writing averages or bra-ket notation, with other applications primarily in mathematics and physics, for use when inline html rendering is desired rather than Template:TeX rendering.

Examples

There is no need to use spaces around the template, due the large spacing in the template glyph.

Examples of bras

The superposition of states can be written ⟨p| +⟨q| +⟨χ| +⟨ψ|, which is inline with the text.

Another superposition of states: ⟨P| +⟨Q| +⟨Φ| +⟨Ψ|, again inline.

The superposition of states can be written {{langle}}p| +{{langle}}q| +{{langle}}χ| +{{langle}}ψ|, which is inline with the text.

Another superposition of states: {{langle}}P| +{{langle}}Q| +{{langle}}Φ| +{{langle}}Ψ|, again inline.
In conjunction with {{Rangle}}

One sum of inner products is ⟨p|qTemplate:Rangle+⟨χ|ψTemplate:Rangle, a real number.

Another sum of inner products is ⟨P|QTemplate:Rangle+⟨Φ|ΨTemplate:Rangle, another real number.

{{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}}

{{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}}

The average of a quantity q may be written ⟨qTemplate:Rangle. The root mean square is then √⟨q2Template:Rangle, i.e. square every value, then average, then take the root.

The average of a quantity ''q'' may be written {{langle}}''q''{{rangle}}. The root mean square is 
then √{{langle}}''q''<sup>2</sup>{{rangle}}, i.e. square every value, then average, then take the root.

See also

For use with {{Rangle}}