"ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ"-ны өөр хувилбарууд

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9-р мөр: 9-р мөр:
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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 ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌<sup>Werner Heisenberg</sup> ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃
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᠃<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 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᠃


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29-р мөр: 29-р мөр:
ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨ<sup>Plank</sup> ᠲᠣᠭᠲᠠᠮᠠᠯ (ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠲᠣᠭᠲᠠᠮᠠᠯ).
ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨ<sup>Plank</sup> 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᠃
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>
 




47-р мөр: 48-р мөр:




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᠃
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>


# '''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᠃
# '''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᠃
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