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wikipedia>Vanisaac: /* See also */clean up per WP:CAT#T and WP:AWBREQ add template:Sandbox other

2020-04-26T21:14:31Z

See also: clean up per WP:CAT#T and WP:AWBREQ add template:Sandbox other

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{{documentation subpage}}
This is the right-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 &#124; (for the pipe symbol), {{tl|langle}}, or {{tl|rangle}} every time.

==Examples==
;Kets

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

Another superposition of states: |P{{rangle}} + |Q{{rangle}} + |Φ{{rangle}} + |Ψ{{rangle}}, again inline.

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

Another superposition of states: |P{{rangle}} + |Q{{rangle}} + |Φ{{rangle}} + |Ψ{{rangle}}, again inline.
</pre>

;Tables (also hidden boxes)

Due to the vertical bar | used in template coding, the html code '''&#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"
|-
! Right bracket alone
! Ket
|-
| Φ{{rangle}} + Ψ{{rangle}}
| |Φ{{rangle}} + |Ψ{{rangle}}
|}

and the wrong way:

{| class="wikitable"
|-
! Right bracket alone
! Ket
|-
| Φ{{rangle}} + Ψ{{rangle}}
| |Φ{{rangle}} + |Ψ{{rangle}}
|}

<pre>
The correct way:

{| class="wikitable"
|-
! Right bracket alone
! Ket
|-
| Φ{{rangle}} + Ψ{{rangle}}
| &#124;Φ{{rangle}} + &#124;Ψ{{rangle}}
|}

and the wrong way:

{| class="wikitable"
|-
! Right bracket alone
! Ket
|-
| Φ{{rangle}} + Ψ{{rangle}}
| |Φ{{rangle}} + |Ψ{{rangle}}
|}
</pre>

;In conjunction with {{tl|langle}}:

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>{{Sandbox other||

[[Category:Mathematical formatting templates]]
}}</includeonly>

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wikipedia>Vanisaac: /* See also */clean up per WP:CAT#T and WP:AWBREQ add template:Sandbox other