Difference between revisions of "Template:Langle/doc"
imported>F=q(E+v^B) |
imported>F=q(E+v^B) |
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==Examples== | ==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> | <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. |
| − | which is inline with the text. | ||
| − | + | Another superposition of states: {{langle}}P| + {{langle}}Q| + {{langle}}Φ| + {{langle}}Ψ|, again inline. | |
| − | Another superposition of states: {{langle | ||
again inline. | again inline. | ||
</pre> | </pre> | ||
;Tables (also hidden boxes) | ;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 becuase of code interference. | ||
The correct way: | The correct way: | ||
| Line 34: | Line 27: | ||
! Bra | ! Bra | ||
|- | |- | ||
| − | | {{langle | + | | {{langle}}Φ + {{langle}}Ψ |
| − | | {{langle | + | | {{langle}}Φ| + {{langle}}Ψ| |
|} | |} | ||
| Line 45: | Line 38: | ||
! Bra | ! Bra | ||
|- | |- | ||
| − | | {{langle | + | | {{langle}}Φ + {{langle}}Ψ |
| − | | {{langle | + | | {{langle}}Φ| + {{langle}}Ψ| |
|} | |} | ||
| Line 57: | Line 50: | ||
! Bra | ! Bra | ||
|- | |- | ||
| − | | {{langle | + | | {{langle}}Φ + {{langle}}Ψ |
| − | | {{langle | + | | {{langle}}Φ| + {{langle}}Ψ| |
|} | |} | ||
| Line 68: | Line 61: | ||
! Bra | ! Bra | ||
|- | |- | ||
| − | | {{langle | + | | {{langle}}Φ + {{langle}}Ψ |
| − | | {{langle | + | | {{langle}}Φ| + {{langle}}Ψ| |
|} | |} | ||
</pre> | </pre> | ||
| Line 75: | Line 68: | ||
;In conjunction with {{tl|rangle}}: | ;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. |
| − | A sum of average values could be {{langle | + | A sum of average values could be {{langle}}P|''E''|Q{{rangle}} + {{langle}}Φ|''p''|Ψ{{rangle}}, another real number. |
<pre> | <pre> | ||
| − | One sum of inner products is {{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 | + | A sum of average values could be {{langle}}P|''E''|Q{{rangle}} + {{langle}}Φ|''p''|Ψ{{rangle}}, another real number. |
</pre> | </pre> | ||
Revision as of 23:47, 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
- 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.
again inline.
- Tables (also hidden boxes)
Due to the vertical bar | used in template coding, the html code | must be used when bra-ket notation is used in tables, else some parts will not show up becuase of code interference.
The correct way:
| Left bracket alone | Bra |
|---|---|
| ⟨Φ + ⟨Ψ | ⟨Φ| + ⟨Ψ| |
and the wrong way:
| Left bracket alone | Bra |
|---|---|
| ⟨Φ + ⟨Ψ | + ⟨Ψ| |
The correct way:
{| class="wikitable"
|-
! Left bracket alone
! Bra
|-
| {{langle}}Φ + {{langle}}Ψ
| {{langle}}Φ| + {{langle}}Ψ|
|}
and the wrong way:
{| class="wikitable"
|-
! Left bracket alone
! Bra
|-
| {{langle}}Φ + {{langle}}Ψ
| {{langle}}Φ| + {{langle}}Ψ|
|}
- In conjunction with {{rangle}}
One sum of inner products is ⟨p|qTemplate:Rangle + ⟨χ|ψTemplate:Rangle, a real number.
A sum of average values could be ⟨P|E|QTemplate:Rangle + ⟨Φ|p|ΨTemplate:Rangle, another real number.
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.
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.