Template:Langle/doc

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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 Template:TeX rendering.

Examples

Using the vertical bar | without scaling:

⟨p|+⟨q|+⟨χ|+⟨ψ|, ⟨p|qTemplate:Rangle+⟨χ|ψTemplate:Rangle

⟨P|+⟨Q|+⟨Φ|+⟨Ψ|, ⟨P|QTemplate:Rangle+⟨Φ|ΨTemplate:Rangle

{{langle}}p|+{{langle}}q|+{{langle}}χ|+{{langle}}ψ|, {{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}}

{{langle}}P|+{{langle}}Q|+{{langle}}Φ|+{{langle}}Ψ|, {{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}}

Using the {{font}} template, the vertical bar can be scaled up to match the height of the angular brackets, with a slightly improved effect:

⟨p|+⟨q|+⟨χ|+⟨ψ|, ⟨p|qTemplate:Rangle+⟨χ|ψTemplate:Rangle

⟨P|+⟨Q|+⟨Φ|+⟨Ψ|, ⟨P|QTemplate:Rangle+⟨Φ|ΨTemplate:Rangle

{{langle}}p{{font|text=||size=17px}}+{{langle}}q{{font|text=||size=17px}}+{{langle}}χ{{font|text=||size=17px}}+{{langle}}ψ

{{font|text=||size=17px}}, {{langle}}p{{font|text=||size=17px}}q{{rangle}}+{{langle}}χ{{font|text=||size=17px}}ψ{{rangle}}


{{langle}}P{{font|text=||size=17px}}+{{langle}}Q{{font|text=||size=17px}}+{{langle}}Φ{{font|text=||size=17px}}+{{langle}}Ψ

{{font|text=||size=17px}}, {{langle}}P{{font|text=||size=17px}}Q{{rangle}}+{{langle}}Φ{{font|text=||size=17px}}Ψ{{rangle}}

See also

For use with {{Rangle}}