Difference between revisions of "Template:Langle/doc"
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==Examples== | ==Examples== | ||
| − | The template has two parameters: | + | The template has two main parameters: |
| − | |||
* '''out''' - content out of the bracket (i.e. behind the vertex of the bracket) | * '''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. | 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|in=p}} | + | 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. |
| − | Another superposition of states: {{langle|in=P}} | + | 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. |
<pre> | <pre> | ||
| − | The superposition of states can be written {{langle|in=p}} | + | The superposition of states can be written {{langle|di=bra|in=p}} + {{langle|di=bra|in=q}} + {{langle|di=bra|in=χ}} + |
| − | which is inline with the text. | + | {{langle|di=bra|in=ψ}}, which is inline with the text. |
| − | Another superposition of states: {{langle|in=P}} | + | 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. | ||
</pre> | </pre> | ||
;In conjunction with {{tl|rangle}}: | ;In conjunction with {{tl|rangle}}: | ||
| − | One sum of inner products is {{langle|in=p}} | + | 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. |
| − | Another sum of inner products is {{langle|in=P}} | + | 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. |
<pre> | <pre> | ||
| − | One sum of inner products is {{langle|in=p}} | + | 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. |
| − | Another sum of inner products is {{langle|in=P}} | + | 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. |
</pre> | </pre> | ||
Revision as of 23:24, 12 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
The template has two main parameters:
- 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 ⟨ is the same as ⟨, becuase di left blank defualts to in.
Notice that {{langle|di=in|in=ψ}} is the same as {{langle|in=ψ}}, becuase '''di''' left blank defualts to '''in'''.
- Examples of bras
The superposition of states can be written ⟨ + ⟨ + ⟨ + ⟨, which is inline with the text.
Another superposition of states: ⟨ + ⟨ + ⟨ + ⟨, again inline.
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.
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.
- In conjunction with {{rangle}}
One sum of inner products is ⟨Template:Rangle+⟨Template:Rangle, a real number.
Another sum of inner products is ⟨Template:Rangle+⟨Template:Rangle, another real number.
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.
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.
The average of a quantity q may be written Template:Rangle or identically ⟨. The root mean square is then √Template:Rangle, i.e. square every value, then average, then take the root.
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.
See also
For use with {{Rangle}}