Difference between revisions of "Template:Langle/doc"
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==Examples== | ==Examples== | ||
| − | + | There is no need to use spaces around the template, due the large spacing in the template glyph. | |
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;Examples of bras | ;Examples of bras | ||
| − | The superposition of states can be written {{langle | + | 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 | + | Another superposition of states: {{langle}}P| +{{langle}}Q| +{{langle}}Φ| +{{langle}}Ψ|, again inline. |
<pre> | <pre> | ||
| − | The superposition of states can be written {{langle | + | The superposition of states can be written {{langle}}p| +{{langle}}q| +{{langle}}χ| +{{langle}}ψ|, which is inline with the text. |
| − | {{langle | ||
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| − | Another superposition of states: {{langle | + | Another superposition of states: {{langle}}P| +{{langle}}Q| +{{langle}}Φ| +{{langle}}Ψ|, again inline. |
| − | again inline. | ||
</pre> | </pre> | ||
| − | ;In conjunction with {{tl| | + | ;In conjunction with {{tl|Rangle}}: |
| − | One sum of inner products is {{langle | + | One sum of inner products is {{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}}, a real number. |
| − | Another sum of inner products is {{langle | + | Another sum of inner products is {{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}}, another real number. |
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<pre> | <pre> | ||
| − | + | {{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}} | |
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| − | + | {{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}} | |
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</pre> | </pre> | ||
| − | The average of a quantity ''q'' may be written | + | 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 | + | The average of a quantity ''q'' may be written {{langle}}''q''{{rangle}}. The root mean square is |
| − | root mean square is then √ | + | 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}}