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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The superposition of states can be written {{langle|in=p}}| + {{langle|in=q}}| + {{langle|in=χ}}| + {{langle|in=ψ}}|, which is inline with the text.
 
The superposition of states can be written {{langle|in=p}}| + {{langle|in=q}}| + {{langle|in=χ}}| + {{langle|in=ψ}}|, which is inline with the text.
  
Another superposition of states: {{langle|in=P}}|+{{langle|in=Q}}+ {{langle|in=Φ}}|+ {{langle|in=Ψ}}|, again inline.
+
Another superposition of states: {{langle|in=P}}| + {{langle|in=Q}}| + {{langle|in=Φ}}| + {{langle|in=Ψ}}|, again inline.
  
 
<pre>
 
<pre>
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Another superposition of states: {{langle|in=P}}|+{{langle|in=Q}}+ {{langle|in=Φ}}|+ {{langle|in=Ψ}}|, again inline.
+
Another superposition of states: {{langle|in=P}}| + {{langle|in=Q}}| + {{langle|in=Φ}}| + {{langle|in=Ψ}}|, again inline.
 
</pre>
 
</pre>
  

Revision as of 15:37, 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 parameters:

  • in - content in the bracket (i.e. behind the vertex of the bracket)
  • out - content out of the bracket (i.e. behind the vertex of the bracket)

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.

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|in=p}}| + {{langle|in=q}}| + {{langle|in=χ}}| + {{langle|in=ψ}}|, 
which is inline with the text.


Another superposition of states: {{langle|in=P}}| + {{langle|in=Q}}| + {{langle|in=Φ}}| + {{langle|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|in=p}}|{{rangle|in=q}}+{{langle|in=χ}}|{{rangle|in=ψ}}, a real number.

Another sum of inner products is {{langle|in=P}}|{{rangle|in=Q}}+{{langle|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}}