ထႅမ်းပလဵတ်ႉ:Langle

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ၽိုၼ်ၵႅမ်မိုဝ်း ထႅမ်းပလဵတ်ႉ[တူၺ်း] [ထတ်း] [ပိုၼ်း] [ၸၢင်း]

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.

တူဝ်ယၢင်ႇ

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&#124; + {{langle}}Ψ&#124;
|}

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.

တူၺ်းပႃး

ၽိုၼ်ၵႅမ်မိုဝ်း တီႈၽၢႆႇၼိူဝ်ၼႆႉ ပဵၼ် ဢၼ် ထွၼ်ဢွၵ်ႇ မႃးတီႈ ထႅမ်းပလဵတ်ႉ:Langle/doc။
ၽူႈမႄးထတ်းၶဝ် ၸၢင်ႈၸၢမ်းတူၺ်းလႆႈ တီႈၼႂ်း ၼႃႈလိၵ်ႈ sandbox လႄႈ testcases ၶွင် ထႅမ်းပလဵတ်ႉ ဢၼ်ၼႆႉ လႆႈယူႇ။
ထႅမ်ပိူင်ထၢၼ်ႈ သႂ်ႇၸူးတီႈ ၼႃႈလိၵ်ႈၽႄ /doc ။ ၼႃႈလိၵ်ႈၽႄ ၶွင် ထႅမ်းပလဵတ်ႉ ဢၼ်ၼႆႉ.