模板:Langle
⟨
.svg){kind=link}
| File:Edit-copy green with red question mark.svg | 此模板的文档不存在、不全面或不能详细描述其功能及/或其代码中的参数。请帮助扩充并改进其文档。 |
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:TᴇX 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[编辑]
- 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.