"ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ"-ны өөр хувилбарууд

Wikibilig-с
(Spelling)
(Category)
 
(Хэрэглэгчид 5 дундын хувилбарууд харагдахгүй)
1-р мөр: 1-р мөр:
<div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'">
<div style="max-height: 80vh; writing-mode: vertical-lr; font-family: 'Noto Sans Mongolian'">
<br>
{| class="wikitable"
|+
|[[File:Hydrogen Density Plots.png|thumb]]
|style = "height: 150px;"|ᠤᠰᠤ ᠲᠥᠷᠦᠭᠴᠢ ᠢᠢᠨ ᠠᠲ᠋ᠣᠮ ᠳ᠋ᠠᠬᠢ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠤ<sup>electron</sup> ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠤᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠵᠢᠷᠤᠭᠯᠠᠯ᠃ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠤ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠨ ᠲᠣᠲᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠲᠤᠯᠠ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠢᠯᠡᠷᠬᠡᠢᠢᠯᠡᠳᠡᠭ᠃ ᠵᠢᠷᠦᠭ ᠳ᠋ᠠᠬᠢ ᠢᠯᠡᠭᠦᠦ ᠭᠡᠷᠡᠯᠲᠡᠢ ᠬᠡᠰᠡᠭ ᠨᠢ ᠢᠯᠡᠭᠦᠦ ᠥᠨᠳᠦᠷ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢ ᠲᠥᠯᠦᠭᠡᠯᠡᠵᠦ ᠪᠠᠢᠢᠨ᠎ᠠ᠃
|}
<br>
ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠪᠣᠯ [[ᠻᠸᠠᠨ᠋ᠲ ᠮᠧᠻᠠᠨᠢᠭ|ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ]] ᠦᠨᠳᠦᠰᠦᠨ [[ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ ᠊ᠤᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠵᠠᠷᠴᠢᠮ ᠊ᠤᠳ|ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠤᠨ]] ᠨᠢᠭᠡ ᠶᠤᠮ᠃ ᠡᠨᠡᠬᠦᠦ ᠵᠠᠷᠴᠢᠮ ᠢᠢᠠᠷ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠬᠣᠣᠰ ᠹᠢᠽᠢᠻ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠨᠤᠭᠦᠳ ᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠨᠠᠷᠢᠨ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ᠃<ref>Heisenberg's Uncertainty Principle. LibreText<sup>TM</sup> Chemistry. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2024/09/17. [https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanics/02._Fundamental_Concepts_of_Quantum_Mechanics/Heisenberg's_Uncertainty_Principle#:~:text=Heisenberg's%20Uncertainty%20Principle%20is%20one,manifested%20as%20non-commuting%20operators. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanics/02._Fundamental_Concepts_of_Quantum_Mechanics/Heisenberg's_Uncertainty_Principle#:~:text=Heisenberg's%20Uncertainty%20Principle%20is%20one,manifested%20as%20non-commuting%20operators.]</ref> ᠨᠢᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠬᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠢᠯᠡᠭᠦᠦ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠨ᠎ᠡ᠂ ᠨᠥᠭᠦᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢᠨ ᠬᠡᠮᠵᠢᠯᠲᠡ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠪᠠᠭᠤᠷᠠᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠪᠣᠯ ᠠᠯᠢᠪᠠ ᠢᠢ ᠳᠤᠷᠠ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠪᠠᠷ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ [[Ньютоны хөдөлгөөний хуулиуд|ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ ᠦᠨ]] ᠰᠢᠰᠲ᠋ᠧᠮ ᠡᠴᠡ ᠻᠸᠠᠨ᠍ᠲ ᠹᠢᠽᠢᠻ ᠢᠯᠭᠠᠭᠳᠠᠬᠤ ᠭᠣᠣᠯ ᠣᠨᠴᠠᠯᠢᠭ ᠶᠤᠮ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠢ 1927 ᠣᠨ ᠳᠤ ᠭᠧᠷᠮᠠᠨ ᠤ ᠹᠢᠽᠢᠻᠴᠢ ᠸᠢᠷᠨᠢᠷ ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌<sup>Werner Heisenberg</sup> ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃
<br>
<br>
__TOC__
__TOC__
<br>
<br>
ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠨᠢᠭᠡ ᠶᠤᠮ᠃ ᠡᠨᠡᠬᠦᠦ ᠵᠠᠷᠴᠢᠮ ᠢᠢᠠᠷ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠬᠣᠣᠰ ᠹᠢᠽᠢᠻ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠨᠤᠭᠦᠳ ᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠨᠠᠷᠢᠨ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ᠃ ᠨᠢᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠬᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠢᠯᠡᠭᠦᠦ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠨ᠎ᠡ᠂ ᠨᠥᠭᠦᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢᠨ ᠬᠡᠮᠵᠢᠯᠲᠡ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠪᠠᠭᠤᠷᠠᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠪᠣᠯ ᠠᠯᠢᠪᠠ ᠢᠢ ᠳᠤᠷᠠ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠪᠠᠷ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠡᠴᠡ ᠻᠸᠠᠨ᠍ᠲ ᠹᠢᠽᠢᠻ ᠢᠯᠭᠠᠭᠳᠠᠬᠤ ᠭᠣᠣᠯ ᠣᠨᠴᠠᠯᠢᠭ ᠶᠤᠮ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠢ 1927 ᠣᠨ ᠳᠤ ᠭᠧᠷᠮᠠᠨ ᠤ ᠹᠢᠽᠢᠻᠴᠢ ᠸᠢᠷᠨᠢᠷ ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌Werner Heisenberg ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃
<br>
<br>
=ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ=
=ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ=
ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠲᠦᠭᠡᠮᠡᠯ ᠵᠢᠱᠢᠶ᠎ᠡ ᠲᠠᠲᠤᠳᠠᠭ ᠬᠡᠯᠪᠡᠷᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠤᠬᠠᠢ ᠳᠤ ᠶᠠᠷᠢᠭᠳᠠᠳᠠᠭ᠃ ᠡᠭᠦᠨ ᠦ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠻ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠯ ᠨᠢ:
<br><br>
{{Horizontal}}
Δ𝑥⋅Δ𝑝≥ℏ/2​
{{Z}}
<br><br>
ᠡ᠊ᠨᠳᠡ:


ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠲᠦᠭᠡᠮᠡᠯ ᠵᠢᠱᠢᠶ᠎ᠡ ᠲᠠᠲᠤᠳᠠᠭ ᠬᠡᠯᠪᠡᠷᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠤᠬᠠᠢ ᠳᠤ ᠶᠠᠷᠢᠭᠳᠠᠳᠠᠭ᠃ ᠡᠭᠦᠨ ᠦ ᠮᠠᠲ᠋ᠧᠮᠠᠲᠢᠻ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠯ ᠨᠢ:


Δx ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃


Δ𝑥⋅Δ𝑝≥ℏ/2​
Δp ᠨᠢ ᠢᠮᠫᠦ᠋ᠯᠰ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃


ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨ<sup>Plank</sup> ᠲᠣᠭᠲᠠᠮᠠᠯ (ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠲᠣᠭᠲᠠᠮᠠᠯ)᠃
<br>
ᠡᠨᠡ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠶᠠᠮᠪᠠᠷ ᠨᠢᠭᠡ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠤᠳᠬ᠎ᠠ ᠡᠴᠡ ᠢᠮᠠᠭᠲᠠ ᠶᠡᠬᠡ ᠪᠤᠶᠤ ᠲᠡᠩᠴᠠᠭᠦᠦ ᠪᠠᠢᠢᠬᠤ ᠶᠣᠰᠤᠲᠠᠢ ᠢᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠭ᠎ᠠ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠦ ᠤᠳᠬ᠎ᠠ ᠢᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠲᠡᠭᠦᠰ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯᠲᠠᠢ ᠮᠡᠳᠡᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ ᠶᠤᠮ᠃<ref>Uncertainty Principle Formula. Toppr 2021. https://www.toppr.com/guides/physics-formulas/uncertainty-principle-formula/</ref>
<br><br>
=ᠵᠦᠢᠯᠴᠢᠯᠡᠪᠡᠰᠦ=
<br>
{| class="wikitable"
|+
|[[File:Quantum mechanics travelling wavefunctions wavelength.svg|thumb]]
|style = "height: 150px;"|ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠴᠢ ᠢᠢᠨ ᠫᠾᠠᠽ<sup>phase</sup>᠃<br>ᠢᠮᠫᠦ᠋ᠯᠰ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ᠃
|}
<br>
1. '''ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ - ᠪᠥᠭᠡᠮᠯᠢᠭ ᠬᠣᠶᠠᠷᠳᠠᠮᠠᠯ ᠴᠢᠨᠠᠷ:''' ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠻ ᠲᠤ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠥᠭᠡᠮᠰ ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠬᠢᠭᠡᠳ ᠪᠥᠭᠡᠮᠯᠢᠭ ᠴᠢᠨᠠᠷ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃ ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠢ [[Цахилгаан соронзон долгионы хуваарь|ᠳᠣᠯᠭᠢᠶᠠᠨ]] ᠭᠡᠵᠦ ᠦᠵᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ ᠲᠠᠢ ᠬᠣᠯᠪᠤᠵᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠪᠠᠯ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠣᠯᠬᠤ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠢ ᠴᠢᠨᠠᠳᠤ ᠲᠣᠭᠲᠤᠭᠠᠭᠰᠠᠨ ᠪᠥᠭᠡᠮ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ (ᠢᠮᠫᠦ᠋ᠯᠰ) ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠡᠴᠡ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠴᠤ ᠪᠠᠢᠢᠨ᠎ᠠ᠃


ᠡ᠊ᠨᠳᠡ:
2. '''ᠵᠥᠪᠬᠡᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢᠢᠡᠷ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠬᠤ ᠦᠭᠡᠢ''': ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠪᠠ ᠴᠠᠭ ᠬᠤᠭᠠᠴᠠᠭ᠎ᠠ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠤᠰᠤᠳ ᠬᠣᠣᠰ ᠬᠤᠪᠢᠰᠠᠭᠴᠢ ᠨᠤᠭᠤᠳ ᠲᠤ ᠪᠠᠰᠠ ᠢᠯᠡᠷᠡᠨ᠎ᠡ᠃ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠡᠨᠧᠷᠭᠢ ᠪᠣᠯᠤᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠬᠡᠮᠵᠢᠭᠰᠡᠨ ᠴᠠᠭ ᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ᠌ :
<br>
{{Horizontal}}
ΔE⋅Δt≥ℏ2
{{Z}}
<br><br>
ᠡᠨᠡ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠨᠡᠩ ᠪᠣᠭᠤᠨᠢ ᠬᠤᠭᠠᠴᠠᠭᠠᠨ ᠤ ᠬᠦᠷᠢᠶᠡᠨ ᠳᠦ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ᠂ ᠬᠠᠷᠢᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠪᠡᠯ ᠴᠠᠭ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠭᠲᠤᠭᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ᠃<ref>John Baez. The Time-Energy Uncertainty Relation. University of California, Riverside 2021/09/26.


https://math.ucr.edu/home/baez/uncertainty.html</ref>
<br>
3. '''ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ''': ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠤᠨ ᠴᠢᠨᠠᠷ ᠪᠣᠯᠬᠤ ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ ᠤᠨ (non-determinism) ᠲᠤᠰᠬᠠᠯ ᠶᠤᠮ᠃ ᠰᠥᠩᠭᠤᠳᠠᠭ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠲᠤ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠪᠦᠬᠢ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠬᠤᠪᠢ᠋ ᠳᠤ ᠡᠨᠡ ᠨᠢ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠡᠭᠢ ᠠᠵᠡᠢ᠃ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲᠧᠮ ᠢ ᠵᠥᠪᠬᠡᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠤᠳᠬ᠎ᠠ ᠪᠠᠷ ᠯᠠ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠳᠠᠭ᠃


Δx ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃
4. '''ᠤᠳᠬ᠎ᠠ ᠤᠴᠢᠷ ᠨᠢ''': ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠲᠠᠯᠠ ᠪᠠᠷ ᠬᠢ ᠻᠣᠫᠢᠨ᠍ᠾᠠᠭᠢᠨ ᠤ ᠲᠠᠢᠢᠯᠠᠪᠦᠷᠢ᠋ ᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠴᠢᠨᠠᠷ ᠨᠢ ᠪᠢᠳᠡᠨ ᠦ ᠬᠡᠮᠵᠢᠬᠦ ᠬᠡᠷᠡᠭᠰᠡᠯ ᠦᠨ ᠲᠡᠭᠦᠰ ᠪᠤᠰᠤ ᠡᠴᠡ ᠡᠭᠦᠳᠡᠯ ᠲᠡᠢ ᠪᠢᠰᠢ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠭᠠᠯᠢ ᠢᠢᠨ ᠰᠠᠭᠤᠷᠢ ᠰᠢᠨᠵᠢ ᠭᠡᠵᠦ ᠥᠬᠦᠯᠡᠳᠡᠭ᠃ ᠥᠭᠡᠷ᠎ᠡ ᠪᠤᠰᠤᠳ ᠲᠠᠢᠢᠯᠠᠪᠦᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠡᠭᠦᠨ ᠲᠡᠢ ᠤᠭᠯᠠᠭᠤᠷᠭ᠎ᠠ ᠪᠠᠷ ᠢᠢᠠᠨ ᠨᠡᠢᠢᠴᠡᠬᠦ ᠪᠠ ᠦᠯᠦ ᠶᠠᠯᠢᠭ ᠢᠯᠭᠠᠭ᠎ᠠ ᠪᠤᠢ᠃


Δp ᠨᠢ ᠢᠮᠫᠦ᠋ᠯᠰ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃


ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨPlank ᠲᠣᠭᠲᠠᠮᠠᠯ (ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠲᠣᠭᠲᠠᠮᠠᠯ).


ᠡᠨᠡ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠶᠠᠮᠪᠠᠷ ᠨᠢᠭᠡ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠤᠳᠬ᠎ᠠ ᠡᠴᠡ ᠢᠮᠠᠭᠲᠠ ᠶᠡᠬᠡ ᠪᠤᠶᠤ ᠲᠡᠩᠴᠠᠭᠦᠦ ᠪᠠᠢᠢᠬᠤ ᠶᠣᠰᠤᠲᠠᠢ ᠢᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠭ᠎ᠠ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠦ ᠤᠳᠬ᠎ᠠ ᠢᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠲᠡᠭᠦᠰ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯᠲᠠᠢ ᠮᠡᠳᠡᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ ᠶᠤᠮ᠃
ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠠᠯᠢᠪᠠ ᠹᠢᠽᠢᠻ ᠰᠢᠰᠲᠧᠮ ᠢ ᠮᠠᠳᠠᠭ ᠦᠭᠡᠢ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠭᠡᠳᠡᠭ ᠲᠦ ᠵᠤᠷᠰᠢᠭᠰᠠᠨ ᠪᠢᠳᠡᠨ ᠦ "ᠰᠣᠩᠭᠤᠳᠠᠭ" (classical) ᠬᠤᠷᠠᠨ ᠮᠡᠳᠡᠬᠦᠢ ᠢᠢ ᠡᠪᠳᠡᠵᠦ᠂ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠳᠦᠷᠰᠦᠯᠡᠭᠳᠡᠬᠦ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠴᠢᠨᠠᠷ ᠤᠨ ᠲᠣᠳᠤ ᠲᠣᠮᠤᠷᠠᠭᠤᠨ ᠢᠯᠡᠷᠡᠯ ᠪᠣᠯᠳᠠᠭ᠃
<br><br>
= ᠨᠡᠷ ‍ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ =


ᠻᠸᠠᠨ᠍ᠲ - quantum


=ᠵᠦᠢᠯᠴᠢᠯᠡᠪᠡᠰᠦ=
ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮ - elementary/fundamental particle
# '''ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ - ᠪᠥᠭᠡᠮᠯᠢᠭ ᠬᠣᠶᠠᠷᠳᠠᠮᠠᠯ ᠴᠢᠨᠠᠷ:''' ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠻ ᠲᠤ ᠡᠯᠧᠻᠲᠷᠣᠨ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠥᠭᠡᠮᠰ ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠬᠢᠭᠡᠳ ᠪᠥᠭᠡᠮᠯᠢᠭ ᠴᠢᠨᠠᠷ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃ ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠭᠡᠵᠦ ᠦᠵᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ ᠲᠠᠢ ᠬᠣᠯᠪᠤᠵᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠪᠠᠯ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠣᠯᠬᠤ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠢ ᠴᠢᠨᠠᠳᠤ ᠲᠣᠭᠲᠤᠭᠠᠭᠰᠠᠨ ᠪᠥᠭᠡᠮ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ (ᠢᠮᠫᠦ᠋ᠯᠰ) ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠡᠴᠡ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠴᠤ ᠪᠠᠢᠢᠨ᠎ᠠ᠃
# '''ᠵᠥᠪᠬᠡᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢᠢᠡᠷ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠬᠤ ᠦᠭᠡᠢ''': ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠪᠠ ᠴᠠᠭ ᠬᠤᠭᠠᠴᠠᠭ᠎ᠠ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠤᠰᠤᠳ ᠬᠣᠣᠰ ᠬᠤᠪᠢᠰᠠᠭᠴᠢ ᠨᠤᠭᠤᠳ ᠲᠤ ᠪᠠᠰᠠ ᠢᠯᠡᠷᠡᠨ᠎ᠡ᠃ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠡᠨᠧᠷᠭᠢ ᠪᠣᠯᠤᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠬᠡᠮᠵᠢᠭᠰᠡᠨ ᠴᠠᠭ ᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ᠌ :


ᠠᠲ᠋ᠣᠮ - atom


ΔE⋅Δt≥ℏ2
ᠳᠣᠯᠭᠢᠶᠠᠨ - wave


ᠪᠥᠭᠡᠮᠰ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠴᠢᠨᠠᠷ - wave-particle duality


ᠡᠨᠡ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠨᠡᠩ ᠪᠣᠭᠤᠨᠢ ᠬᠤᠭᠠᠴᠠᠭᠠᠨ ᠤ ᠬᠦᠷᠢᠶᠡᠨ ᠳᠦ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ᠂ ᠬᠠᠷᠢᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠪᠡᠯ ᠴᠠᠭ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠭᠲᠤᠭᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ᠃
ᠲᠣᠳᠣᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠶᠢᠨ ᠵᠠᠷᠴᠢᠮ - uncertainty principle


# '''ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ''': ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠤᠨ ᠴᠢᠨᠠᠷ ᠪᠣᠯᠬᠤ ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ ᠤᠨ (non-determinism) ᠲᠤᠰᠬᠠᠯ ᠶᠤᠮ᠃ ᠰᠥᠩᠭᠤᠳᠠᠭ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠲᠤ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠪᠦᠬᠢ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠬᠤᠪᠢ᠋ ᠳᠤ ᠡᠨᠡ ᠨᠢ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠡᠭᠢ ᠠᠵᠡᠢ᠃ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲᠧᠮ ᠢ ᠵᠥᠪᠬᠡᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠤᠳᠬ᠎ᠠ ᠪᠠᠷ ᠯᠠ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠳᠠᠭ᠃
ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ - inequality
# '''ᠤᠳᠬ᠎ᠠ ᠤᠴᠢᠷ ᠨᠢ''': ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠲᠠᠯᠠ ᠪᠠᠷ ᠬᠢ ᠻᠣᠫᠢᠨ᠍ᠾᠠᠭᠢᠨ ᠤ ᠲᠠᠢᠢᠯᠠᠪᠦᠷᠢ᠋ ᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠴᠢᠨᠠᠷ ᠨᠢ ᠪᠢᠳᠡᠨ ᠦ ᠬᠡᠮᠵᠢᠬᠦ ᠬᠡᠷᠡᠭᠰᠡᠯ ᠦᠨ ᠲᠡᠭᠦᠰ ᠪᠤᠰᠤ ᠡᠴᠡ ᠡᠭᠦᠳᠡᠯ ᠲᠡᠢ ᠪᠢᠰᠢ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠭᠠᠯᠢ ᠢᠢᠨ ᠰᠠᠭᠤᠷᠢ ᠰᠢᠨᠵᠢ ᠭᠡᠵᠦ ᠥᠬᠦᠯᠡᠳᠡᠭ᠃ ᠥᠭᠡᠷ᠎ᠡ ᠪᠤᠰᠤᠳ ᠲᠠᠢᠢᠯᠠᠪᠦᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠡᠭᠦᠨ ᠲᠡᠢ ᠤᠭᠯᠠᠭᠤᠷᠭ᠎ᠠ ᠪᠠᠷ ᠢᠢᠠᠨ ᠨᠡᠢᠢᠴᠡᠬᠦ ᠪᠠ ᠦᠯᠦ ᠶᠠᠯᠢᠭ ᠢᠯᠭᠠᠭ᠎ᠠ ᠪᠤᠢ᠃


ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ - classical physics


ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠠᠯᠢᠪᠠ ᠹᠢᠽᠢᠻ ᠰᠢᠰᠲᠧᠮ ᠢ ᠮᠠᠳᠠᠭ ᠦᠭᠡᠢ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠭᠡᠳᠡᠭ ᠲᠦ ᠵᠤᠷᠰᠢᠭᠰᠠᠨ ᠪᠢᠳᠡᠨ ᠦ "ᠰᠣᠩᠭᠤᠳᠠᠭ" (classical) ᠬᠤᠷᠠᠨ ᠮᠡᠳᠡᠬᠦᠢ ᠢᠢ ᠡᠪᠳᠡᠵᠦ᠂ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠳᠦᠷᠰᠦᠯᠡᠭᠳᠡᠬᠦ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠴᠢᠨᠠᠷ ᠤᠨ ᠲᠣᠳᠤ ᠲᠣᠮᠤᠷᠠᠭᠤᠨ ᠢᠯᠡᠷᠡᠯ ᠪᠣᠯᠳᠠᠭ᠃
ᠮᠠᠭᠠᠳᠯᠠᠯ - probability
<br>
<br>
=ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ=
<div style="writing-mode: horizontal-tb; "><References/>
[[Ангилал:ᠹᠢᠽᠢᠻ]]

11:10, 18 Есдүгээр сар 2024-ий байдлаарх одоогийн засвар


ᠤᠰᠤ ᠲᠥᠷᠦᠭᠴᠢ ᠢᠢᠨ ᠠᠲ᠋ᠣᠮ ᠳ᠋ᠠᠬᠢ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠤelectron ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠤᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠵᠢᠷᠤᠭᠯᠠᠯ᠃ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠤ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠨ ᠲᠣᠲᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠲᠤᠯᠠ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠢᠯᠡᠷᠬᠡᠢᠢᠯᠡᠳᠡᠭ᠃ ᠵᠢᠷᠦᠭ ᠳ᠋ᠠᠬᠢ ᠢᠯᠡᠭᠦᠦ ᠭᠡᠷᠡᠯᠲᠡᠢ ᠬᠡᠰᠡᠭ ᠨᠢ ᠢᠯᠡᠭᠦᠦ ᠥᠨᠳᠦᠷ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢ ᠲᠥᠯᠦᠭᠡᠯᠡᠵᠦ ᠪᠠᠢᠢᠨ᠎ᠠ᠃


ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠨᠢᠭᠡ ᠶᠤᠮ᠃ ᠡᠨᠡᠬᠦᠦ ᠵᠠᠷᠴᠢᠮ ᠢᠢᠠᠷ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠬᠣᠣᠰ ᠹᠢᠽᠢᠻ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠨᠤᠭᠦᠳ ᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠨᠠᠷᠢᠨ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ᠃[1] ᠨᠢᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠬᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠢᠯᠡᠭᠦᠦ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠨ᠎ᠡ᠂ ᠨᠥᠭᠦᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢᠨ ᠬᠡᠮᠵᠢᠯᠲᠡ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠪᠠᠭᠤᠷᠠᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠪᠣᠯ ᠠᠯᠢᠪᠠ ᠢᠢ ᠳᠤᠷᠠ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠪᠠᠷ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠡᠴᠡ ᠻᠸᠠᠨ᠍ᠲ ᠹᠢᠽᠢᠻ ᠢᠯᠭᠠᠭᠳᠠᠬᠤ ᠭᠣᠣᠯ ᠣᠨᠴᠠᠯᠢᠭ ᠶᠤᠮ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠢ 1927 ᠣᠨ ᠳᠤ ᠭᠧᠷᠮᠠᠨ ᠤ ᠹᠢᠽᠢᠻᠴᠢ ᠸᠢᠷᠨᠢᠷ ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌Werner Heisenberg ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃



ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ[засварлах | кодоор засварлах]

ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠲᠦᠭᠡᠮᠡᠯ ᠵᠢᠱᠢᠶ᠎ᠡ ᠲᠠᠲᠤᠳᠠᠭ ᠬᠡᠯᠪᠡᠷᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠤᠬᠠᠢ ᠳᠤ ᠶᠠᠷᠢᠭᠳᠠᠳᠠᠭ᠃ ᠡᠭᠦᠨ ᠦ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠻ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠯ ᠨᠢ:

Δ𝑥⋅Δ𝑝≥ℏ/2​

ᠡ᠊ᠨᠳᠡ:


Δx ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃

Δp ᠨᠢ ᠢᠮᠫᠦ᠋ᠯᠰ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃

ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨPlank ᠲᠣᠭᠲᠠᠮᠠᠯ (ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠲᠣᠭᠲᠠᠮᠠᠯ)᠃
ᠡᠨᠡ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠶᠠᠮᠪᠠᠷ ᠨᠢᠭᠡ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠤᠳᠬ᠎ᠠ ᠡᠴᠡ ᠢᠮᠠᠭᠲᠠ ᠶᠡᠬᠡ ᠪᠤᠶᠤ ᠲᠡᠩᠴᠠᠭᠦᠦ ᠪᠠᠢᠢᠬᠤ ᠶᠣᠰᠤᠲᠠᠢ ᠢᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠭ᠎ᠠ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠦ ᠤᠳᠬ᠎ᠠ ᠢᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠲᠡᠭᠦᠰ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯᠲᠠᠢ ᠮᠡᠳᠡᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ ᠶᠤᠮ᠃[2]

ᠵᠦᠢᠯᠴᠢᠯᠡᠪᠡᠰᠦ[засварлах | кодоор засварлах]


ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠹᠦᠨ᠍ᠻᠴᠢ ᠢᠢᠨ ᠫᠾᠠᠽphase
ᠢᠮᠫᠦ᠋ᠯᠰ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ᠃


1. ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ - ᠪᠥᠭᠡᠮᠯᠢᠭ ᠬᠣᠶᠠᠷᠳᠠᠮᠠᠯ ᠴᠢᠨᠠᠷ: ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠻ ᠲᠤ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠥᠭᠡᠮᠰ ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠬᠢᠭᠡᠳ ᠪᠥᠭᠡᠮᠯᠢᠭ ᠴᠢᠨᠠᠷ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃ ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠭᠡᠵᠦ ᠦᠵᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ ᠲᠠᠢ ᠬᠣᠯᠪᠤᠵᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠪᠠᠯ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠣᠯᠬᠤ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠢ ᠴᠢᠨᠠᠳᠤ ᠲᠣᠭᠲᠤᠭᠠᠭᠰᠠᠨ ᠪᠥᠭᠡᠮ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ (ᠢᠮᠫᠦ᠋ᠯᠰ) ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠡᠴᠡ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠴᠤ ᠪᠠᠢᠢᠨ᠎ᠠ᠃

2. ᠵᠥᠪᠬᠡᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢᠢᠡᠷ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠬᠤ ᠦᠭᠡᠢ: ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠪᠠ ᠴᠠᠭ ᠬᠤᠭᠠᠴᠠᠭ᠎ᠠ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠤᠰᠤᠳ ᠬᠣᠣᠰ ᠬᠤᠪᠢᠰᠠᠭᠴᠢ ᠨᠤᠭᠤᠳ ᠲᠤ ᠪᠠᠰᠠ ᠢᠯᠡᠷᠡᠨ᠎ᠡ᠃ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠡᠨᠧᠷᠭᠢ ᠪᠣᠯᠤᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠬᠡᠮᠵᠢᠭᠰᠡᠨ ᠴᠠᠭ ᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ᠌ :
ΔE⋅Δt≥ℏ2

ᠡᠨᠡ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠨᠡᠩ ᠪᠣᠭᠤᠨᠢ ᠬᠤᠭᠠᠴᠠᠭᠠᠨ ᠤ ᠬᠦᠷᠢᠶᠡᠨ ᠳᠦ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ᠂ ᠬᠠᠷᠢᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠪᠡᠯ ᠴᠠᠭ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠭᠲᠤᠭᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ᠃[3]
3. ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ: ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠤᠨ ᠴᠢᠨᠠᠷ ᠪᠣᠯᠬᠤ ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ ᠤᠨ (non-determinism) ᠲᠤᠰᠬᠠᠯ ᠶᠤᠮ᠃ ᠰᠥᠩᠭᠤᠳᠠᠭ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠲᠤ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠪᠦᠬᠢ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠬᠤᠪᠢ᠋ ᠳᠤ ᠡᠨᠡ ᠨᠢ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠡᠭᠢ ᠠᠵᠡᠢ᠃ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲᠧᠮ ᠢ ᠵᠥᠪᠬᠡᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠤᠳᠬ᠎ᠠ ᠪᠠᠷ ᠯᠠ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠳᠠᠭ᠃

4. ᠤᠳᠬ᠎ᠠ ᠤᠴᠢᠷ ᠨᠢ: ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠲᠠᠯᠠ ᠪᠠᠷ ᠬᠢ ᠻᠣᠫᠢᠨ᠍ᠾᠠᠭᠢᠨ ᠤ ᠲᠠᠢᠢᠯᠠᠪᠦᠷᠢ᠋ ᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠴᠢᠨᠠᠷ ᠨᠢ ᠪᠢᠳᠡᠨ ᠦ ᠬᠡᠮᠵᠢᠬᠦ ᠬᠡᠷᠡᠭᠰᠡᠯ ᠦᠨ ᠲᠡᠭᠦᠰ ᠪᠤᠰᠤ ᠡᠴᠡ ᠡᠭᠦᠳᠡᠯ ᠲᠡᠢ ᠪᠢᠰᠢ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠭᠠᠯᠢ ᠢᠢᠨ ᠰᠠᠭᠤᠷᠢ ᠰᠢᠨᠵᠢ ᠭᠡᠵᠦ ᠥᠬᠦᠯᠡᠳᠡᠭ᠃ ᠥᠭᠡᠷ᠎ᠡ ᠪᠤᠰᠤᠳ ᠲᠠᠢᠢᠯᠠᠪᠦᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠡᠭᠦᠨ ᠲᠡᠢ ᠤᠭᠯᠠᠭᠤᠷᠭ᠎ᠠ ᠪᠠᠷ ᠢᠢᠠᠨ ᠨᠡᠢᠢᠴᠡᠬᠦ ᠪᠠ ᠦᠯᠦ ᠶᠠᠯᠢᠭ ᠢᠯᠭᠠᠭ᠎ᠠ ᠪᠤᠢ᠃


ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠠᠯᠢᠪᠠ ᠹᠢᠽᠢᠻ ᠰᠢᠰᠲᠧᠮ ᠢ ᠮᠠᠳᠠᠭ ᠦᠭᠡᠢ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠭᠡᠳᠡᠭ ᠲᠦ ᠵᠤᠷᠰᠢᠭᠰᠠᠨ ᠪᠢᠳᠡᠨ ᠦ "ᠰᠣᠩᠭᠤᠳᠠᠭ" (classical) ᠬᠤᠷᠠᠨ ᠮᠡᠳᠡᠬᠦᠢ ᠢᠢ ᠡᠪᠳᠡᠵᠦ᠂ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠳᠦᠷᠰᠦᠯᠡᠭᠳᠡᠬᠦ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠴᠢᠨᠠᠷ ᠤᠨ ᠲᠣᠳᠤ ᠲᠣᠮᠤᠷᠠᠭᠤᠨ ᠢᠯᠡᠷᠡᠯ ᠪᠣᠯᠳᠠᠭ᠃

ᠨᠡᠷ ‍ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ[засварлах | кодоор засварлах]

ᠻᠸᠠᠨ᠍ᠲ - quantum

ᠡᠭᠡᠯ ᠪᠥᠭᠡᠮ - elementary/fundamental particle

ᠠᠲ᠋ᠣᠮ - atom

ᠳᠣᠯᠭᠢᠶᠠᠨ - wave

ᠪᠥᠭᠡᠮᠰ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠴᠢᠨᠠᠷ - wave-particle duality

ᠲᠣᠳᠣᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠶᠢᠨ ᠵᠠᠷᠴᠢᠮ - uncertainty principle

ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ - inequality

ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ - classical physics

ᠮᠠᠭᠠᠳᠯᠠᠯ - probability

ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ[засварлах | кодоор засварлах]