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


	ᠤᠰᠤ ᠲᠥᠷᠦᠭᠴᠢ ᠢᠢᠨ ᠠᠲ᠋ᠣᠮ ᠳ᠋ᠠᠬᠢ ᠡᠯᠧᠻᠲ᠋ᠷᠣᠨ ᠤ^electron 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 ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌^{Werner 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 ᠤᠨ^Plank 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 ᠫᠾᠠᠽ^phase᠃ 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]

↑ Heisenberg's Uncertainty Principle. LibreText^TM 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.
↑ Uncertainty Principle Formula. Toppr 2021. https://www.toppr.com/guides/physics-formulas/uncertainty-principle-formula/
↑ John Baez. The Time-Energy Uncertainty Relation. University of California, Riverside 2021/09/26. https://math.ucr.edu/home/baez/uncertainty.html

[1] Heisenberg's Uncertainty Principle. LibreText^TM 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.

[2] Uncertainty Principle Formula. Toppr 2021. https://www.toppr.com/guides/physics-formulas/uncertainty-principle-formula/

[3] John Baez. The Time-Energy Uncertainty Relation. University of California, Riverside 2021/09/26. https://math.ucr.edu/home/baez/uncertainty.html

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@@ 1-р мөр: / 1-р мөр: @@
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+{| class="wikitable"
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+|[[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᠃
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 __TOC__
 <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>
 =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>
+. '''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:
+. '''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>
+. '''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᠃
+. '''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>
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+=ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ=
+<div style="writing-mode: horizontal-tb; "><References/>
+[[Ангилал:ᠹᠢᠽᠢᠻ]]

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

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ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ[засварлах | кодоор засварлах]

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