模板:Rangle/doc

1. REDIRECT Template:改進使用說明

This is the right-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

Kets

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

Another superposition of states: |P{{rangle}} + |Q{{rangle}} + |Φ{{rangle}} + |Ψ{{rangle}}, 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:

Right bracket alone	Ket
Φ⟩ + Ψ⟩	|Φ⟩ + |Ψ⟩

and the wrong way:

Right bracket alone	Ket
Φ⟩ + Ψ⟩	Φ⟩ + |Ψ⟩

The correct way: 

{| class="wikitable"
|-
! Right bracket alone 
! Ket
|-
| Φ{{rangle}} + Ψ{{rangle}}
| |Φ{{rangle}} + |Ψ{{rangle}}
|}

and the wrong way:

{| class="wikitable"
|-
! Right bracket alone 
! Ket
|-
| Φ{{rangle}} + Ψ{{rangle}}
| |Φ{{rangle}} + |Ψ{{rangle}}
|}

In conjunction with {{langle}}

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.