Template:Rangle
⟩
This is the right-handed angular bracket used for writingaveragesorbra–ket notation,with other applications primarily inmathematicsandphysics,for use when inline html rendering is desired rather thanTeXrendering.
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[edit]
- 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 quantityqmay 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.