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  • ၵဵဝ်ႇၵပ်း ဝီႇၶီႇၽီးတီးယႃး
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ဝီႇၶီႇၽီးတီးယႃး

ထႅမ်းပလဵတ်ႉ:Langle

  • ၽႃႇသႃႇ
  • ပႂ်ႉတူၺ်း
  • မႄးထတ်း

⟨

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

မႄးထတ်း
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.

တူၺ်းပႃး

မႄးထတ်း
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  • e
Math templates
  • Functions
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Functions
  • elementary arithmetic
  • precision
  • val (value)
Numeral systems
  • {{#invoke:BaseConvert|XtoY}}
  • binary
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  • quaternary
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  • roman
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Conversions
convert many units (see: list)
cvt abbreviated {{convert}}
convinfobox {{convert}} for infoboxes
bbl to t barrels of oil to tonnes
long ton long hundredweights, quarters and pounds to kilograms;
long tons and hundredweights to pounds and metric tons
miles-chains miles and chains to kilometres linking "chains"
rndfrac decimals to fractions
decdeg degrees, minutes, and seconds to decimal degrees
deg2dms decimal degrees to degrees, minutes, and seconds
deg2hms decimal degrees to hour angle (in hours, minutes, and seconds)
hms2deg hour angle (in hours, minutes, and seconds) to decimal degrees
inflation calculate inflation of Consumer Price Index-related prices
pop density population density in an area
track gauge railway track gauges
Notation and formatting
bigmath bigger font to match TeX \displaystyle (standalone formulas only)
  • bra-ket
  • braket
  • bra
  • ket
bra–ket notation
ceil, floor calculations :mw:Help:#expr; formatting indicators ⌈3.14⌉, ⌊3.14⌋ (no calculation performed)
frac slant fractions 3⁄5 (not for maths/science articles; use standing or upright fractions {{sfrac}} instead)
intmath integral symbols
  • langle
  • rangle
  • angbr
angular brackets
  • ldelim
  • rdelim
multiline delimiters (2–5 lines inclusive)
abs absolute values (paired vertical lines)
math short text-based formulas
mathcal [mathematical] calligraphic font; alternative to LaTeX \mathcal{...}
mvar individual italicized maths variables in normal text
  • overline
  • underline
a line set above/below a sequence of characters
  • overset
  • underset
arbitrary characters/diacritics set above/below one another
pars parentheses that can be resized (∑)
sfrac “standing” or upright fractions 3/5 (use in maths/science articles instead of{{frac}})
  • sub
  • sup
  • su
subscripts and superscripts
tmath Wrap TeX in <math> tags
tombstone symbol indicating the end of a proof
val measurement values, uncertainties and units
vec various overarrows, underarrows, etc.
  • Boxes
  • Tags
  • Notices
BoxesTags
  • calculation results
  • calculus
  • Infobox mathematics function
  • functions
  • metricate
  • undue precision
  • units attention
Category Category · Module:Math
ၽိုၼ်ၵႅမ်မိုဝ်း တီႈၽၢႆႇၼိူဝ်ၼႆႉ ပဵၼ် ဢၼ် ထွၼ်ဢွၵ်ႇ မႃးတီႈ ထႅမ်းပလဵတ်ႉ:Langle/doc။ (ထတ်း | ပိုၼ်း)
ၽူႈမႄးထတ်းၶဝ် ၸၢင်ႈၸၢမ်းတူၺ်းလႆႈ တီႈၼႂ်း ၼႃႈလိၵ်ႈ sandbox (သၢင်ႈ | mirror) လႄႈ testcases (သၢင်ႈ) ၶွင် ထႅမ်းပလဵတ်ႉ ဢၼ်ၼႆႉ လႆႈယူႇ။
ထႅမ်ပိူင်ထၢၼ်ႈ သႂ်ႇၸူးတီႈ ၼႃႈလိၵ်ႈၽႄ /doc ။ ၼႃႈလိၵ်ႈၽႄ ၶွင် ထႅမ်းပလဵတ်ႉ ဢၼ်ၼႆႉ.
ဢဝ်ၶိုၼ်းမႃးတီႈ "https://shn.wikipedia.org/w/index.php?title=ထႅမ်းပလဵတ်ႉ:Langle&oldid=50214"
Last edited on 19 ၼူဝ်ႇဝႅမ်ႇပႃႇ 2021, at 05:23

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