模板:Langle
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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 TeX rendering.
This is used in the {{braket}} template. When creating bra or ket vectors, or inner products, use {{Braket}} to save the trouble of typing | (for the pipe symbol), {{langle}}, or {{rangle}} every time.
Examples
[編輯]- 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.
- 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 because 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|q⟩ + ⟨χ|ψ⟩, a real number.
A sum of average values could be ⟨P|E|Q⟩ + ⟨Φ|p|Ψ⟩, 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 ⟨q⟩. The root mean square is then √⟨q2⟩, 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.
上述文件嵌入自Template:Langle/doc。 (編輯 | 歷史) 編者可以在本模板的沙盒 (建立 | 鏡像)和測試樣例 (建立)頁面進行實驗。 請在/doc子頁面中添加分類。本模板的子頁面。 |