Difference between revisions of "Template:Langle/doc"

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This is the left-handed angular bracket used for writing [[average]]s or [[bra–ket notation]], with other applications primarily in [[mathematics]] and [[physics]], for use when inline html rendering is desired rather than [[TeX]] rendering.
 
 
 
This is used in the {{tl|braket}} template. When creating bra or ket vectors, or inner products, use {{tl|Braket}} to save the trouble of typing | (for the pipe symbol), {{tl|langle}}, or {{tl|rangle}} every time.
 
 
 
==Examples==
 
;Bras
 
 
 
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.
 
 
 
<pre>
 
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.
 
</pre>
 
 
 
;Tables (also hidden boxes)
 
 
 
Due to the vertical bar | used in template coding, the html code '''&amp;#124;''' must be used when bra–ket notation is used in tables, else some parts will not show up because of code interference.
 
 
 
The correct way:
 
 
 
{| class="wikitable"
 
|-
 
! Left bracket alone
 
! Bra
 
|-
 
| {{langle}}Φ + {{langle}}Ψ
 
| {{langle}}Φ&#124; + {{langle}}Ψ&#124;
 
|}
 
 
 
and the wrong way:
 
 
 
{| class="wikitable"
 
|-
 
! Left bracket alone
 
! Bra
 
|-
 
| {{langle}}Φ + {{langle}}Ψ
 
| {{langle}}Φ| + {{langle}}Ψ|
 
|}
 
 
 
<pre>
 
The correct way:
 
 
 
{| class="wikitable"
 
|-
 
! Left bracket alone
 
! Bra
 
|-
 
| {{langle}}Φ + {{langle}}Ψ
 
| {{langle}}Φ&amp;#124; + {{langle}}Ψ&amp;#124;
 
|}
 
 
 
and the wrong way:
 
 
 
{| class="wikitable"
 
|-
 
! Left bracket alone
 
! Bra
 
|-
 
| {{langle}}Φ + {{langle}}Ψ
 
| {{langle}}Φ| + {{langle}}Ψ|
 
|}
 
</pre>
 
 
 
;In conjunction with {{tl|rangle}}:
 
 
 
One sum of inner products is {{langle}}p|q{{rangle}} + {{langle}}χ|ψ{{rangle}}, a real number.
 
 
 
A sum of average values could be {{langle}}P|''E''|Q{{rangle}} + {{langle}}Φ|''p''|Ψ{{rangle}}, another real number.
 
 
 
<pre>
 
One sum of inner products is {{langle}}p|q{{rangle}} + {{langle}}χ|ψ{{rangle}}, a real number.
 
 
 
A sum of average values could be {{langle}}P|''E''|Q{{rangle}} + {{langle}}Φ|''p''|Ψ{{rangle}}, another real number.
 
</pre>
 
 
 
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>
 
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>
 
 
 
==See also==
 
{{Math templates|notation}}
 
 
 
<includeonly>
 
<!-- CATEGORIES HERE, THANKS -->
 
[[Category:Mathematical formatting templates]]
 
</includeonly>
 

Revision as of 22:05, 13 August 2016

MT